Slope and y = mx + b · lesson

Slope from two points

💡 Slope is the change in y divided by the change in x, subtracting in the same order.

Slope = (change in y) ÷ (change in x). People say rise over run.

Subtract the y's, and subtract the x's in the same order. A negative slope means the line goes down to the right.

🧠 Let's work it out

Find the slope through (1, 2) and (4, 14).

What do you think comes next?

💡 In y = mx + b, the number times x is the slope and the number added on is the y-intercept.

In y = mx + b, m is the slope. It is the number multiplied by x.

b is the y-intercept. It is where the line crosses the y-axis, when x = 0.

The terms may be in a different order. In y = 5 − 4x, the slope is −4 and the intercept is 5.

🧠 Let's work it out

What are the slope and intercept of y = 5 − 4x?

What do you think comes next?

💡 Find the slope, find the y-intercept, then put both into y = mx + b.

If you know m and b, just fill them in.

If you know two points, find the slope first. If one point has x = 0, its y is b. If not, see the next card.

🧠 Let's work it out

Write the line through (0, −2) and (3, 4).

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💡 Put the slope and one point into y = mx + b, then solve for b.

If you know the slope and any point, you can find b.

Put the point's x and y and the slope into y = mx + b. Then solve for b.

🧠 Let's work it out

A line has slope 4 and goes through (3, 10). Find b.

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💡 To put an equation in slope-intercept form, solve it for y.

An equation like 3x + y = 8 is not in y = mx + b form yet.

Move the x term to the other side. Do the same thing to both sides.

🧠 Let's work it out

Rewrite 3x + y = 8 in the form y = mx + b.

What do you think comes next?