6:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Heart of Algebra: Linear Equations (2 variables) — Quiz 1\",\"description\":\"Linear equations in two variables practice for PSAT 8/9.\",\"url\":\"https://theschoolofmathematics.com/quiz/psat-8-9-linear-equations-2-variables-1\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Heart of Algebra: Linear Equations (2 variables)\"}}"}}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://theschoolofmathematics.com\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Quizzes\",\"item\":\"https://theschoolofmathematics.com/quiz\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Heart of Algebra: Linear Equations (2 variables) — Quiz 1\",\"item\":\"https://theschoolofmathematics.com/quiz/psat-8-9-linear-equations-2-variables-1\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","div",null,{"className":"container mx-auto px-4 py-8 md:py-12","children":[["$","div",null,{"className":"mb-12","children":["$undefined",["$","div",null,{"className":"mb-8","children":["$","h1",null,{"className":"text-4xl md:text-5xl lg:text-6xl font-bold text-gray-900 mb-4","children":"Heart of Algebra: Linear Equations (2 variables) — Quiz 1"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","div",null,{"className":"text-lg md:text-xl text-gray-700 mb-6 leading-relaxed prose prose-lg max-w-none","dangerouslySetInnerHTML":{"__html":"

Linear equations in two variables practice for PSAT 8/9.

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Linear equations in two variables practice for PSAT 8/9.

"},"excerpt":{"rendered":"

Linear equations in two variables practice for PSAT 8/9.

"},"explanation":null,"metaTitle":null,"metaDescription":null,"featured_media":0,"featured_media_url":"$undefined","acf":{"duree_estimee":"$undefined","niveau_difficulte":"$undefined","categorie":"Heart of Algebra: Linear Equations (2 variables)","nombre_questions":10,"score_minimum":80,"ordre_questions":"Fixe","questions":[{"id":"cmrk8exyq0wd8jg8wanp0g4l0","texte_question":"$19","type_question":"TexteLibre","explication":"

From the graph, the line crosses the $$y$$-axis at $$-8$$.

So, the y-intercept is:

$$b=-8$$

The line also crosses the $$x$$-axis at about $$-8$$.

Use the two points:

$$(-8,0)$$ and $$(0,-8)$$

Find the slope.

$$m=\\frac{-8-0}{0-(-8)}$$

$$m=\\frac{-8}{8}$$

$$m=-1$$

So, the equation is:

$$y=-x-8$$

Final answer: $$y=-x-8$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

y=-x-8

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8exyv0wdbjg8wgxhhk2l1","texte_question":"

A line in the $$xy$$-plane has a slope of $$\\frac{3}{4}$$ and passes through the point $$(0,-2)$$. Which equation represents this line?

","type_question":"QCM","explication":"

Use slope-intercept form.

$$y=mx+b$$

The slope is:

$$m=\\frac{3}{4}$$

The line passes through $$(0,-2)$$.

This means the $$y$$-intercept is:

$$b=-2$$

Substitute

$$m=\\frac{3}{4}$$ and $$b=-2$$.

$$y=\\frac{3}{4}x-2$$

Final answer: $$y=\\frac{3}{4}x-2$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$y=\\frac{3}{4}x-2$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$y=-\\frac{3}{4}x-2$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$y=\\frac{4}{3}x-2$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$y=\\frac{3}{4}x+2$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8exyx0wdhjg8weyk46nbp","texte_question":"

Line $$k$$ is defined by $$y=-5x+7$$. Line $$j$$ is parallel to line $$k$$ in the $$xy$$-plane. What is the slope of line $$j$$?

","type_question":"QCM","explication":"

The equation of line $$k$$ is:

$$y=-5x+7$$

This is in slope-intercept form.

$$y=mx+b$$

The slope is the coefficient of $$x$$.

$$m=-5$$

Parallel lines have the same slope.

So, line $$j$$ also has slope: $$-5$$

Final answer: $$-5$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$-5$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$5$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{1}{5}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$-\\frac{1}{5}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8exz00wdnjg8wswluaqhl","texte_question":"

On a $$180$$-mile trip, Sofia drove at an average speed of $$60$$ miles per hour for the first $$x$$ hours. She then completed the trip at an average speed of $$40$$ miles per hour for the remaining $$y$$ hours. If $$x=2$$, what is the value of $$y$$?

","type_question":"TexteLibre","explication":"

Distance equals rate times time.

For the first part of the trip: $$60x$$

For the second part of the trip: $$40y$$

The total distance is $$180$$ miles.

$$60x+40y=180$$

Substitute $$x=2$$.

$$60(2)+40y=180$$

$$120+40y=180$$

Subtract $$120$$ from both sides.

$$40y=60$$

Divide by $$40$$.

$$y=\\frac{60}{40}$$

Simplify.

$$y=\\frac{3}{2}$$

Final answer: $$\\frac{3}{2}$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

3/2

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8exz30wdqjg8wzle7shub","texte_question":"

Line $$p$$ is defined by $$4y-8x=16$$. Line $$r$$ is perpendicular to line $$p$$. What is the slope of line $$r$$?

","type_question":"QCM","explication":"

Rewrite the equation of line $$p$$ in slope-intercept form.

$$4y-8x=16$$

Add $$8x$$ to both sides.

$$4y=8x+16$$

Divide every term by $$4$$.

$$y=2x+4$$

So, the slope of line $$p$$ is: $$2$$

Perpendicular lines have slopes that are negative reciprocals.

The negative reciprocal of $$2$$ is: $$-\\frac{1}{2}$$

Final answer: $$-\\frac{1}{2}$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$\\frac{1}{2}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$-\\frac{1}{2}$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$2$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$-2$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8exz60wdwjg8wc78esomn","texte_question":"

Line $$\\ell$$ is defined by $$2x+5y=10$$. Line $$n$$ is perpendicular to line $$\\ell$$. What is the slope of line $$n$$?

","type_question":"TexteLibre","explication":"

Rewrite the equation in slope-intercept form.

$$2x+5y=10$$

Subtract $$2x$$ from both sides.

$$5y=-2x+10$$

Divide every term by $$5$$.

$$y=-\\frac{2}{5}x+2$$

The slope of line $$\\ell$$ is: $$-\\frac{2}{5}$$

A perpendicular line has the negative reciprocal slope.

The negative reciprocal of $$-\\frac{2}{5}$$ is: $$\\frac{5}{2}$$

Final answer: $$\\frac{5}{2}$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

5/2

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8exz90wdzjg8w0qvsrtxi","texte_question":"

When a line is graphed in the $$xy$$-plane, it has an $$x$$-intercept of $$(3,0)$$ and a $$y$$-intercept of $$(0,-6)$$. What is the slope of the line?

","type_question":"QCM","explication":"

Use the two intercept points: $$(3,0)$$ and $$(0,-6)$$

Find the slope.

$$m=\\frac{-6-0}{0-3}$$

$$m=\\frac{-6}{-3}$$

$$m=2$$

Final answer: $$2$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$-2$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$2$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$-\\frac{1}{2}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{1}{2}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8exzc0we5jg8wa6j276z9","texte_question":"

A school has a $$3$$-acre field and a $$12$$-acre forest. The total number of trees is $$2,100$$. The equation $$3x+12y=2100$$ represents this situation. Which is the best interpretation of $$y$$?

","type_question":"QCM","explication":"

The equation is:

$$3x+12y=2100$$

The school has a $$3$$-acre field and a $$12$$-acre forest.

The term $$3x$$ represents the trees in the field. Since $$3$$ is the number of acres in the field, $$x$$ represents the average number of trees per acre in the field. The term $$12y$$ represents the trees in the forest. Since $$12$$ is the number of acres in the forest, $$y$$ represents the average number of trees per acre in the forest.

Final answer: $$\\text{The average number of trees per acre in the forest}$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$\\text{The total number of trees in the forest}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\text{The number of acres in the forest}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\text{The average number of trees per acre in the forest}$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\text{The average number of trees per acre in the field}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8exzf0webjg8wfbter3f4","texte_question":"

Lena made $$40$$ cups of lemonade. She poured the lemonade into $$x$$ small cups and $$y$$ large cups. The equation $$2x+5y=40$$ represents this situation. Which is the best interpretation of $$2x$$?

","type_question":"QCM","explication":"

The equation is:

$$2x+5y=40$$

The variable $$x$$ represents the number of small cups.

Each small cup holds $$2$$ cups of lemonade.

So, $$2x$$ represents the total amount of lemonade, in cups, poured into the small cups.

Final answer: $$\\text{The total number of cups in the small cups}$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$\\text{The number of small cups used}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\text{The number of large cups used}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\text{The total number of cups in the small cups}$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\text{The total number of cups in the large cups}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8exzh0wehjg8wc07cgnpi","texte_question":"$1a","type_question":"QCM","explication":"

Use the two points from the table: $$(2,10)$$ and $$(5,-2)$$

Find the slope.

$$m=\\frac{-2-10}{5-2}$$

$$m=\\frac{-12}{3}$$

$$m=-4$$

Use slope-intercept form.

$$y=-4x+b$$

Substitute the point $$(2,10)$$.

$$10=-4(2)+b$$

$$10=-8+b$$

Add $$8$$ to both sides.

$$18=b$$

Final answer: $$18$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

","correcte":true,"explication":"","imageUrl":"$undefined"}]}]},"categories":["heart-of-algebra-linear-equations-two-variables"],"date":"2026-06-04T09:04:45.720Z","modified":"2026-07-14T05:49:50.829Z"}}],false,["$","div",null,{"className":"mt-10 mb-12","aria-label":"Advertisement","children":["$","div",null,{"className":"my-8 ","children":["$","$L1b",null,{"adSlot":"1234567890","adFormat":"auto","fullWidthResponsive":true,"style":{"minHeight":"250px"}}]}]}]]}]}]]

Heart of Algebra: Linear Equations (2 variables) — Quiz 1

Questions in this quiz (10)