Study on the flyISEE UpperMathematics AchievementLinear equations and graphs

Mathematics Achievement

Linear equations and graphs — ISEE Upper practice questions

  • 97 practice questions in the app
  • Free

What this topic is

Slope-intercept form, y equals m x plus b, is the key format for Linear equations and graphs.

Rewriting an equation into that form reveals the slope directly, though fractions or extra constants on either side must be cleared first. Intercepts come from setting x or y to zero; together with the origin they form a right triangle whose area is half the product of the intercepts.

Some questions ask which equation passes through two given points, which can be checked by substituting both points into each choice. Two different lines with the same slope are parallel and never meet, and a horizontal line has slope zero.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

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?

Show answer

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 12⋅6⋅9=27.

Question 2Easier

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

Show answer

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 3Mid

What is the slope of the line 3x−1=y2+4?

Show answer

Answer: C — 6

Subtract 4: 3x−5=y2. Multiply by 2: y=6x−10. The slope is 6.

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 97 Linear equations and graphs questions in the app

More ISEE Upper topics

Harder than the exam: ISEE Upper Challenge · Competition-style problems

Everything on the ISEE Upper