Front

What is the point-slope form of a linear equation?

Back

The point-slope form of a linear equation is given by y - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.

Front

How do you calculate the slope between two points (x_1, y_1) and (x_2, y_2)?

Back

The slope (m) is calculated using the formula m = (y_2 - y_1) / (x_2 - x_1).

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the slope of a line that rises 2 units for every 3 units it runs?

Back

The slope of the line is 2/3.

Front

How can you convert the equation 5x + y = -10 into slope-intercept form?

Back

To convert to slope-intercept form (y = mx + b), solve for y: y = -5x - 10.

Front

What is the slope of a line that passes through the points (1, 2) and (3, 6)?

Back

The slope is m = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the slope-intercept form y = mx + b.

Front

How do you find the y-intercept from the equation y - 3 = 2(x + 4)?

Back

To find the y-intercept, set x = 0: y - 3 = 2(0 + 4) => y = 8 + 3 => y = 11. The y-intercept is (0, 11).

Front

What is the formula for finding the slope of a line given two points?

Back

The formula is m = (y_2 - y_1) / (x_2 - x_1).

Front

How do you write the equation of a line in point-slope form given a point and a slope?

Back

Use the formula y - y_1 = m(x - x_1), substituting the point (x_1, y_1) and the slope m.