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Algebra · Linear Equations And Inequalities

SAT Linear Equations And Inequalities Practice Questions (Free + Explanations) | Quiz 2

Question 12345 of 5

Question 1 of 5

On a city map, a straight bike path is shown by a line that passes through the points and . If represents the path's height above sea level at a horizontal distance of miles, what is the value of when ?

Explanation

The line passes through and , so its slope is . That means the height increases by for each increase of mile in . Starting from when , at the value of is . So the correct answer is .

Concept summary

When a line is described by two points, find the slope from the change in over the change in , then use it with a known point to determine another value on the line.

Question 2 of 5

If , what is the value of ?

Explanation

First divide both sides of by to get . Then add to find . Since the question asks for , the value is .

Concept summary

Undo operations in order to solve for a variable, then evaluate the expression the problem asks for.

Question 3 of 5

A line passes through the points and . Which equation is equivalent to the equation of this line written in slope-intercept form?

Explanation

The line crosses the -axis at , so the -intercept is . Its slope is

In slope-intercept form, , so the equation is .

Concept summary

To write a line in slope-intercept form, find the slope from two points and use the point where the line crosses the -axis as the intercept.

Question 4 of 5

On the coordinate plane, a line passes through and . Which equation represents this line?

Explanation

The line crosses the -axis at , so its -intercept is . From to , the change in is and the change in is , so the slope is . Therefore, the equation is .

Concept summary

To write an equation from points on a line, find the slope from the change in over the change in , then use the -intercept in slope-intercept form .

Question 5 of 5

At a school store, notebooks cost dollars each and pens cost dollars each. One notebook and one pen together cost dollars. If a pen costs dollars, which equation can be used to find the cost of one notebook?

Explanation

The total cost is modeled by the system information . Since a pen costs , substitute into the equation to get . That equation can be used to find the notebook cost.

Concept summary

Write a linear equation from the situation, then substitute the known value from the system to get an equation in one variable.

Your results

0of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

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Your results

1of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

2of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

3of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

4of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

5of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice