Review · Q5 · Slope-intercept equation from m and b

01 Mini-Lesson Video

▸ 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.

02 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.

Writing slope-intercept form v1

A line has slope m = 4 and y-intercept (0, −7).

Write the equation in slope-intercept form.

y =

Writing slope-intercept form v2

A line has slope m = −1/2 and y-intercept (0, 5).

Write the equation in slope-intercept form.

y =

Writing slope-intercept form — zero slope v3

A line has slope m = 0 and y-intercept (0, 6).

Write the equation in slope-intercept form.

y =

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.

03 How to Solve It

y = mx + b
plug in m, plug in b, done

Slope-intercept form has two slots. The slope (m) goes in front of x; the intercept (b) is the constant. The two numbers come straight from the prompt — no algebra required.

1

m = 4, intercept (0, −7).

Read the prompt: m = 4, b = −7 (the y-coordinate of the intercept).

Drop them into y = mx + b:

y = 4 x + (-7)

Clean it up: + (−7) becomes − 7. Final answer: y = 4x − 7.

2

m = −1/2, intercept (0, 5).

m = −1/2, b = 5.

y = (-1/2) x + 5

Most write this as y = −(1/2)x + 5 or y = −x/2 + 5 — all three are the same equation.

3

m = 0, intercept (0, 6).

Slope of zero is the special case: the line is horizontal. The mx term disappears because 0 · x = 0.

y = 0 x + 6 = 6

Final answer: y = 6. The line is at y = 6 for every x — flat across.

▸ COMMON SLIPStudents take the intercept point (0, 5) and use the 0 instead of the 5. The fix: the y-intercept b is the y-coordinate (the second number), not the x-coordinate. The first number is always 0 because the intercept lives on the y-axis. What you want is the second.

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Hands-on practiceTry the Line ExplorerSlide m and b, watch the line move. Same shape every Q5 on the review.

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04 Practice — Step by Step

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

1

Pull m from the prompt.

Practice problem: Slope m = −3, y-intercept (0, 4). Write y = mx + b. What's the value of m?

m =

2

Pull b from the intercept.

The intercept is (0, 4). What's b?

b =

3

Assemble y = mx + b.

With m = −3 and b = 4, what's the equation? Type it as y=mx+b with no spaces (e.g. y=2x+5 or y=-x-3).

equation:

▸ NICE WORK

You walked the slope-intercept move end to end.

Same three steps every time: pull m, pull b, drop them into y = mx + b. No algebra, no manipulation — just two numbers in two slots.