Graphing a line
Plot a line from its slope-intercept equation. Find the intercept, then use slope to step out a second point.
A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.
ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.
Graph the line:
y = 2x + 3
y-intercept:
second point:
Graph the line:
y = (3/4)x − 2
y-intercept:
second point:
Graph the line:
y = −x + 4
y-intercept:
second point:
b tells you where; m tells you which way
Graph y = 2x + 3.
Read off the equation: m = 2, b = 3. The y-intercept is (0, 3) — start there.
Slope 2 means rise 2, run 1 (because 2 = 2/1). From (0, 3), go up 2 and right 1.
Two points, one line. Draw it through them.
Graph y = (3/4)x − 2.
Now m = 3/4, b = −2. Y-intercept is (0, −2).
Slope is a fraction: 3/4 means rise 3, run 4. From (0, −2), go up 3 and right 4.
When the slope is a fraction, use it as-is. The denominator is your run, the numerator is your rise.
Graph y = −x + 4.
m = −1 (the coefficient of x is −1, even though it's not written explicitly), b = 4. Y-intercept (0, 4).
Negative slope means the line goes down. From (0, 4), go down 1 and right 1 (because −1 = −1/1).
Negative slope = down and right (or up and left — same line either way).
Walk through this practice problem one step at a time. Each step unlocks the next.
Identify the y-intercept.
Identify the slope.
Step out the second point.
You walked the graphing move end to end.
Same three steps every time: read b and plot (0, b), read m as rise/run and step out a second point, draw the line through both. The numbers change; the move doesn't.