MAT-144 · Mathematical Reasoning Topic 01 · Linear Functions
Topic 01 · Review · Q4

Graphing a line

Plot a line from its slope-intercept equation. Find the intercept, then use slope to step out a second point.

▸ VIDEO COMING SOON

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.

Graphing a line v1

Graph the line:

y = 2x + 3

y-intercept:
second point:

Graphing a line — fractional slope v2

Graph the line:

y = (3/4)x − 2

y-intercept:
second point:

Graphing a line — negative slope v3

Graph the line:

y = −x + 4

y-intercept:
second point:

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.
y = mx + b
b tells you where; m tells you which way
Plot the y-intercept first: it's the point (0, b). From there, slope m = rise/run gives you a second point — go up by the rise, right by the run. Connect the two.
1

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.

(0, 3) → (1, 5)

Two points, one line. Draw it through them.

2

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.

(0, −2) → (4, 1)

When the slope is a fraction, use it as-is. The denominator is your run, the numerator is your rise.

3

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).

(0, 4) → (1, 3)

Negative slope = down and right (or up and left — same line either way).

▸ COMMON SLIPStudents reverse rise and run, going right by the numerator and up by the denominator. The fix: slope = rise / run. Top is rise (up or down), bottom is run (right). For 3/4, that's up 3 and right 4 — never up 4 and right 3.
Hands-on practiceTry the Line ExplorerSlide m and b, watch the line move. Same shape every Q4 on the review.

Walk through this practice problem one step at a time. Each step unlocks the next.

1

Identify the y-intercept.

Practice problem: Graph y = (1/2)x − 3. What's the y-intercept?
b =
2

Identify the slope.

What's the slope (m) in y = (1/2)x − 3? Type your answer as a decimal (e.g. 0.5).
m =
3

Step out the second point.

Starting from the intercept (0, −3) and using slope 1/2 (rise 1, run 2), what's the y-value of the next point at x = 2?
y =
▸ NICE WORK

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.

Q3 Q5