Lesson 4.2 Homework

Front

What is the Point-Slope form of a linear equation?

Back

The Point-Slope form is given by the equation: 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 convert a Point-Slope equation to Slope-Intercept form?

Back

To convert from Point-Slope form (y - y_1 = m(x - x_1)) to Slope-Intercept form (y = mx + b), solve for y.

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

Given the point (4, -7) and slope -1/4, write the equation in Point-Slope form.

Back

y + 7 = -1/4(x - 4)

Front

Given the point (10, 5) and slope -3, write the equation in Point-Slope form.

Back

y - 5 = -3(x - 10)

Front

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

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1) = (3 - 1) / (3 - 2) = 2.

Front

How do you find the y-intercept from the Slope-Intercept form?

Back

In the Slope-Intercept form y = mx + b, the y-intercept is the value of b.

Front

Write the equation in Slope-Intercept form for the line through (-2, -3) and (5, 4).

Back

y = x - 1

Front

Write the equation in Slope-Intercept form for the line through (2, 1) and (3, 3).

Back

y = 2x - 3

Front

What does the slope of a line represent?

Back

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