Free video lesson

How to Read Slope From a Graph on the SAT

Every line on the SAT is hiding inside just two numbers — the slope and the y-intercept. Learn to read them, and you can graph any line (or check it in Desmos) in seconds.

Math · Linear functions2:10Published July 4, 2026

On YouTube: SAT Slope: Read the Graph

What this lesson covers

  • Read the slope (m) and y-intercept (b) straight off y = mx + b
  • Graph a line with no table: start at b, then rise-over-run
  • Speed-graph it on the Digital SAT with Desmos — and pull exact points
  • Practice: a line through (0, 4) with slope −1/2
  • The three traps that cost easy points

Questions worked in the video

  1. 0:29Graph the line y = 2x − 3. Where does it cross each axis?
  2. 1:09A line passes through (0, 4) with slope −1/2. Write its equation and find its x-intercept.

Worked examples

The questions the video works, written out: the setup, each step, the answer and the trap.

0:29Example 1

Graph the line y=2x−3y = 2x - 3. Where does it cross the y-axis, how steep is it, and where does it cross the x-axis?

  1. Match the equation to y=mx+by = mx + b: m = 2 and b = -3. Both answers are already sitting in the equation.
  2. b is the y-intercept, so the line crosses the y-axis at (0, -3). Put the first dot there.
  3. m is the slope, rise over run: 2=21\displaystyle 2 = \frac{2}{1}, so from (0, -3) go up 2 and right 1 to (1, -1), then again to (2, 1). Connect the dots; no table needed.
  4. For the x-intercept set y = 0: 0=2x−30 = 2x - 3, so 2x=32x = 3 and x=32\displaystyle x = \frac{3}{2}. The line crosses the x-axis at (1.5, 0). In Desmos, type the equation and click the crossing to read (1.5, 0) exactly.
  5. Check: 2(1.5)−3=02(1.5) - 3 = 0 and 2(1)−3=−12(1) - 3 = -1, so (1.5, 0) and (1, -1) both sit on the line.

Answer: y-intercept (0, -3), slope 2, x-intercept (1.5, 0)

b tells you where the line starts on the y-axis and m tells you how fast it climbs, so the graph comes straight from the two numbers. The trap is reading b as the x-intercept and marking (-3, 0); b is always the y-intercept, and the x-intercept needs the extra step of setting y to 0.

1:09Example 2

A line passes through (0, 4) with slope −12\displaystyle -\frac{1}{2}. Write its equation and find its x-intercept.

  1. The point (0, 4) is on the y-axis, so it is the y-intercept: b = 4. The slope is given: m=−12\displaystyle m = -\frac{1}{2}.
  2. Drop both into y=mx+by = mx + b: y=−12x+4\displaystyle y = -\frac{1}{2}x + 4.
  3. Set y = 0 for the x-intercept: 0=−12x+4\displaystyle 0 = -\frac{1}{2}x + 4, so 12x=4\displaystyle \frac{1}{2}x = 4 and x = 8. The line crosses the x-axis at (8, 0).
  4. To graph it, a slope of −12\displaystyle -\frac{1}{2} means down 1 for every 2 to the right: (0, 4), (2, 3), (4, 2), (6, 1), (8, 0).
  5. Check: −12(8)+4=−4+4=0\displaystyle -\frac{1}{2}(8) + 4 = -4 + 4 = 0.

Answer: y=−12x+4\displaystyle y = -\frac{1}{2}x + 4, x-intercept (8, 0)

A point with x = 0 hands you b for free, and the slope is m, so the equation is two substitutions. The trap is dropping the minus sign on a falling line and writing y=12x+4\displaystyle y = \frac{1}{2}x + 4, which gives an x-intercept of (-8, 0); a line that falls from left to right must have a negative slope.

Chapters

Lesson transcript

The narration of the video, word for word, under its chapter headings.

0:00Two numbers hide in every line

Welcome to SAT Climb. Every line on a graph is hiding in just two numbers. Read them, and you can graph any line — or check it in Desmos — in seconds.

0:16The setup: y = 2x − 3

Here's the equation: y = 2x − 3. Where does this line cross the y-axis, and how steep is it? Both answers are already in the equation.

0:29Read it off the equation

Split it. b is your y-intercept — start at −3 on the y-axis. m is the slope: rise over run. 2 means up 2, right 1. Connect the dots — graphed, no table.

0:49Speed-graph it in Desmos

On the Digital SAT, you don't even draw it. Type y = 2x − 3 and the line appears. Click where it crosses an axis — Desmos hands you the exact point.

1:09Your turn

Your turn. A line through (0, 4) with slope −½. Write its equation, then find where it crosses the x-axis. Type it in Desmos for the shortcut.

1:35Three traps

Three traps. Flipping rise over run. Dropping the minus sign on a line that falls. And reading b as the x-intercept — it's the y-intercept.

1:56Recap

Slope and lines: solved. Read a line from its equation, check it in Desmos, and these become the fastest points on the test. Start free at satclimb.com.

Read the written version: the Linear functions strategy guide, then try 25 hard Linear functions questions with full explanations. Both are free, no account needed.

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