Linear Equations

The slope of a nonvertical line passing through the points (x₁, y₁) and (x₂, y₂) is

matches

“The line is going uphill, so the slope is positive. Starting at (-1, -1) you go up 1 and right 3, so the slope is .”

The linear equation y = mx + b is written in slope-intercept form. The slope is m. The y-intercept is b.

Example

matches m = 3.

“From one point on the graph, you move up 3 and right 1 to the second point, so the slope is 3.”

Warm-Up

y = 3x - 2 matches .

“From the graph, the y-intercept is -2 and the slope is 3. So the equation is y = 3x - 2.”

A solution of a linear equation is an ordered pair whose values make the equation true. To find a solution, pick a value for x, substitute it into the equation, and solve for y

y = 3x - 7; (2,      ) is a solution. matches -1

“Replace with 2; 3 times 2 is 6. 6 minus 7 is -1, so the answer is -1.”