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Linear Equations

Slope Given Two Points

Background

The slope of a nonvertical line passing through the
points (x_{1}, y_{1}) and (x_{2}, y_{2}) is

Warm-Up

matches

â€œThe line is going uphill, so the slope is positive.
Starting at (-1, -1) you go up 1 and right 3,
so the slope is
.â€

Linear Equations in Slope-Intercept Form

Background

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

Example

Warm-Up

matches
m = 3.

â€œFrom one point on the graph, you move up 3 and
right 1 to the second point, so the slope is 3.â€

Warm-Up

y = 3x - 2 matches
.

â€œFrom the graph, the y-intercept is -2 and the slope
is 3. So the equation is y = 3x - 2.â€

Finding Solutions to the Equation y = mx + b

Background

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

Warm-Up

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

â€œReplace with 2; 3 times 2 is 6. 6 minus 7 is -1,
so the answer is -1.â€