Same Math › Algebra 1 · grades 8–10 › Slope-intercept form
What is slope-intercept form?
Slope-intercept form, y = mx + b, describes a line with two numbers: m is the slope (how steep, rise over run) and b is the y-intercept (where it crosses the y-axis). To graph y = 2x − 1, start at −1 on the y-axis, then go up 2 and over 1, and repeat. Kids also work backwards from two points to the equation.
- b: start on the y-axis here.
- m: rise over run, from that starting point.
- Connect the points into a straight line.
Why schools teach it
Two numbers tell the whole story
Eighth graders derive y = mx + b (8.EE.B.6), and Algebra 1 students graph lines and read their features (HSF.IF.C.7a). In a word problem, m is the rate and b is the starting amount: a $20 sign-up plus $5 a week is y = 5x + 20.
Starting at b and stepping with the slope beats making a table of points, and it makes mistakes easy to spot.
At the kitchen table
What to say, and what to skip
Say this
Where does it cross the y-axis?
That's b.What's the rise over the run?
That's m. Down means negative.With two points: what's the change in y over the change in x?
Plug in a point. Does it work?
Skip this
- Starting the graph at the origin.Start at b on the y-axis.
- Run over rise.Slope is rise (up/down) over run (left/right).
- Forgetting the negative slope.Going down to the right means m is negative.
See it in action
Writing the line through (1, 5) and (3, 9)
Slope: change in y over change in x
(9 − 5) ÷ (3 − 1) = 2Plug in one point to find b
5 = 2(1) + b, so b = 3Write it
y = 2x + 3
Check with the other point: 2(3) + 3 = 9 ✓.
Free practice sheet
Make a slope-intercept sheet
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Parents also ask
What if the slope is a fraction, like 2/3?
Up 2, over 3. Fractions are the easiest slopes to graph.
What if there's no b, like y = 3x?
Then b = 0 and the line goes through the origin.
What about equations like 2x + y = 5?
Solve for y first: y = −2x + 5. Then read m and b.
What's point-slope form?
y − y₁ = m(x − x₁). It's another way to write the same line, handy with a point and a slope.