Eighth Grade · Math · week 5

Slope-intercept form

Write and interpret linear equations in slope-intercept form, y = (slope)x + (y-intercept).

Slope-intercept form is written y = mx + b, where m is the slope and b is the y-intercept -- the value of y when x = 0. Say it out loud: "y equals the slope times x, plus the starting value."

If you are given the slope and ONE point (not the y-intercept itself), substitute that point into y = mx + b and solve for b -- the exact same equation-solving skill from the last few weeks, just with letters standing in for the number you eventually plug in.

📋 For the teacher
Teach it (10–15 min):
  • Say slope-intercept form as a sentence every time: "y equals the slope times x, plus the starting value."
  • b is a "head start" -- the value of y before x has done anything, at x = 0.
  • If given a graph directly, b can just be READ off where the line crosses the y-axis -- no equation-solving needed at all.
  • Have them verify their final equation by testing it against the original point they were given.
Talk about it:
  • Why does plugging in x = 0 always give you back b?
  • If you are given a graph, how do you find b without any equation-solving?
  • In y = -2x + 7, what does the negative slope tell you about the line's direction?

Mastery looks like: Given a slope and any point (or a graph), they correctly build y = mx + b, and can read m and b out of an equation already in that form.

Common stumbles: Substituting x and y into the wrong spots (swapping them); forgetting that b is added AFTER multiplying m by x, not before.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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