MAT-144 · Mathematical Reasoning
Topic 01 · Linear Functions
Slope-intercept equation from m and b
Given a y-intercept and a slope, write the equation in slope-intercept form.
01
Worked Example Video
Every step of Slope-intercept equation from m and b explained on video. Pause anywhere; the embed scrolls independently of the page.
YOUTUBE
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
A line has slope m = 4 and y-intercept (0, −7). Write the equation in slope-intercept form.
y =
✓
Right — m = 4 goes with x; b = −7 is the constant. Answer: y = 4x − 7.
✗
Slope goes in front of x, intercept goes at the end. m = 4, b = −7 → y = 4x − 7.
Writing slope-intercept form
A line has slope m = −1/2 and y-intercept (0, 5). Write the equation in slope-intercept form.
y =
✓
Right — m = −1/2 sits in front of x; b = 5 is the constant. Answer: y = −(1/2)x + 5.
✗
m = −1/2, b = 5. The equation is y = −(1/2)x + 5. Fractions in the slope slot are fine — just leave them as-is.
Writing slope-intercept form — zero slope
A line has slope m = 0 and y-intercept (0, 6). Write the equation in slope-intercept form.
y =
✓
Right — when m = 0, the x-term drops out entirely. Answer is just y = 6. That’s a horizontal line through (0, 6).
✗
When m = 0, the mx term is 0 and disappears. The answer is just the constant: y = 6.
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
The Rule
Slope-intercept form is y = mx + b
slope goes with x, intercept goes at the end
m and b come straight from the prompt
no algebra required
Two slots to fill. The slope (m) sits in front of x; the intercept value (b) is the constant on the end. If b is negative, write it as −7, not + −7. See it live: change m and b, watch the equation update →
Common slip
When b is negative, students write y = 4x + −7 instead of y = 4x − 7. Both mean the same thing, but ALEKS wants the clean form. When m = 0, the x-term drops out entirely — the answer is just y = b.
04
Practice — Step by Step
Practice this problem step by step
A line has slope m = −3 and y-intercept (0, 2). Write the equation in slope-intercept form.
Identify m and b
Which value is b (the intercept)?
The intercept is (0, 2). b is the y-value of that point.
✓
Right — the intercept is (0, 2), so b = 2.
✗
Not quite — try again.
Write the equation
Plug m = −3 and b = 2 into y = mx + b.
y =
y = (m)x + (b). Plug in −3 for m and 2 for b.
✓
Perfect. y = −3x + 2. Same move every time — plug m into the coefficient slot, plug b into the constant slot.
✗
Not quite. m = −3 goes in front of x, b = 2 is the constant. Answer: y = −3x + 2.
🎉
You wrote the slope-intercept equation.
Same move every time: slope goes with x, intercept goes at the end. ALEKS will change the numbers — whole, fraction, negative, or zero — but the two slots are always the same.