4.2 study guide

Front

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

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Front

Write the slope-intercept form of the line with slope -3/4 and y-intercept 3.

Back

y = (-3/4)x + 3.

Front

Given f(-3) = -1 and f(-2) = 4, write the linear function in slope-intercept form.

Back

f(x) = 5x + 14.

Front

Given f(-1) = 2 and f(3) = 3, write the linear function in slope-intercept form.

Back

f(x) = (1/4)x + (9/4).

Front

Given f(-2) = 1 and f(1) = 7, write the linear function in slope-intercept form.

Back

f(x) = 2x + 5.

Front

What is point-slope form of a linear equation?

Back

Point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

Write the point-slope form of the line that passes through (-1, -2) with slope -1.

Back

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

Front

What is the significance of the slope in a linear function?

Back

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