Linear equations and graphs — ISEE Upper practice questions

Linear equations and graphs on the ISEE Upper Mathematics Achievement section covers slope, intercepts, and matching a line to points or to the coordinate axes. A student must rearrange an equation into a useful form, find slope from two points or from an equation, identify which line contains given points, and use intercepts to find a quantity such as the area of the triangle formed with the axes. Questions are multiple choice and often leave the equation in a messy form so that mixing up slope and intercepts or skipping the algebra leads to a nearby wrong option; choices are usually a number or the equation of a line.

Section: Mathematics Achievement 47 questions on the paper
97 practice questions in the app

Sample questions

Question 1

The line $3x+2y=18$ crosses the $x$ -axis and the $y$ -axis, forming a right triangle with the coordinate axes. What is the area of that triangle?

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Answer: C — 27

The $x$ -intercept is 6 because $3x=18$ . The $y$ -intercept is 9 because $2y=18$ . The triangle's legs along the axes have lengths 6 and 9, so the area is $\dfrac{1}{2}\cdot6\cdot9=27$ .

Question 2

Which line contains the two points $(-2,-1)$ and $(4,11)$ ?

A $y = 2x + 3$
B $y = 2x - 3$
C $y = \dfrac{1}{2}x$
D $y = -2x + 3$

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Answer: A — $y = 2x + 3$

The slope is $(11-(-1))/(4-(-2))=2$ . Substituting $(-2,-1)$ gives the intercept 3, so the line is $y=2x+3$ .

Question 3

What is the slope of the line $3x - 1 = \dfrac{y}{2} + 4$ ?

A $\dfrac{1}{2}$
B3
C6
D12

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Answer: C — 6

Subtract 4: $3x - 5 = \dfrac{y}{2}$ . Multiply by 2: $y = 6x - 10$ . The slope is 6.

Practice 97 Linear equations and graphs questions in the app

Linear equations and graphs — ISEE Upper practice questions

Sample questions

More ISEE Upper topics

Mathematics Achievement