MAT-144 · Mathematical Reasoning
Topic 07 · Taxes & Stocks
Graphing a line
Plot a line from its slope-intercept equation. Find the intercept, then use slope to step out a second point.
01
Worked Example Video
Every step of Graphing a line explained on video. Pause anywhere; the embed scrolls independently of the page.
YOUTUBE
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What This Looks Like on ALEKS
ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.
Graphing a line
Graph the line y = 2x + 3. What is the y-intercept as an ordered pair?
y-intercept =
✓
Right — b = 3, so the y-intercept is (0, 3). From there, use slope 2 (rise 2, run 1) to step to (1, 5).
✗
The y-intercept is at x = 0. In y = 2x + 3, b = 3, so the y-intercept is (0, 3).
Graphing a line — fractional slope
Graph the line y = (3/4)x − 2. What is the y-intercept as an ordered pair?
y-intercept =
✓
Right — b = −2, so the y-intercept is (0, −2). From there, slope 3/4 means rise 3, run 4 → second point (4, 1).
✗
The y-intercept is at x = 0. In y = (3/4)x − 2, b = −2, so the y-intercept is (0, −2).
Graphing a line — negative slope
Graph the line y = −x + 4. What is the y-intercept as an ordered pair?
y-intercept =
✓
Right — b = 4, so the y-intercept is (0, 4). Slope −1 means rise −1, run 1 → second point (1, 3).
✗
The y-intercept is at x = 0. In y = −x + 4, b = 4, so the y-intercept is (0, 4).
Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.
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The Rule
Equation is y = mx + b
the y-intercept is (0, b)
Slope m = rise/run
from (0, b), go up rise, right run
Plot the y-intercept first — it’s always at x = 0. From there, use the slope as a rise-over-run recipe to step out a second point. Two points define the line. See it live: m = 3, b = −2 →
Common slip
Students swap rise and run. Slope 3/4 means rise = 3, run = 4 (numerator on top, denominator on bottom). A slope of just 2 is really 2/1 — rise 2, run 1.
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Practice — Step by Step
Practice this problem step by step
Graph the line y = 3x − 2.
Find b (the y-intercept value)
In y = 3x − 2, what is b?
In y = mx + b, b is the number added (or subtracted) after mx. In y = 3x − 2, that’s the −2.
✓
Right — b = −2. The y-intercept is the point (0, −2).
✗
Not quite — try again.
Find m (the slope)
In y = 3x − 2, what is m? (Remember: 3 as a slope means 3/1 — rise 3, run 1.)
m is the coefficient of x — the number sitting in front of x.
✓
Right — m = 3, which means rise = 3 and run = 1.
✗
Not quite — try again.
Plot the line
Drag point A to the y-intercept (0, −2), then drag point B to a second point on y = 3x − 2. The line will follow. When both points sit on the line, click Check my graph.
Drag both points onto the correct positions.
Place point A at (0, −2), then place point B by going up 3, right 1 from A — that lands at (1, 1).
✓
Nailed it — both points land on y = 3x − 2. Two points, one line.
✗
Not quite. From the y-intercept (0, −2), slope 3 means up 3 and right 1 — landing at (1, 1). Try again.
🎉
You graphed the line end to end.
Same three moves every time: read b (the y-intercept), read m (rise/run), step out to the second point. Then draw the line through the two dots. ALEKS will use different values of m and b — but the move is identical.