Finding Slope and Line Equations

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, calculated as the change in y (rise) over the change in x (run).

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If a line has a slope of 2, what is the slope of a line perpendicular to it?

Back

The slope of a line perpendicular to it is -1/2 (negative reciprocal).

Front

Write the equation of a line in slope-intercept form given a slope of 3 and a y-intercept of -4.

Back

y = 3x - 4.

Front

What is the slope of the line represented by the equation y = -5x + 2?

Back

The slope is -5.

Front

How do you convert the point-slope form of a line to slope-intercept form?

Back

Start with y - y1 = m(x - x1) and solve for y.

Front

What is the point-slope form of a line with slope -1 passing through the point (2, 3)?

Back

y - 3 = -1(x - 2).

Front

Find the slope of the line that passes through the points (3, 7) and (6, 10).

Back

Slope = (10 - 7) / (6 - 3) = 1.