In the xy-plane, line m passes through the point (4, -2) and has a y-intercept of 6. What … — GRE General Test

In the $xy$ -plane, line $m$ passes through the point $(4, -2)$ and has a $y$ -intercept of $6$ . What is the slope of line $m$ ?

Answer: -2

The slope of line

m

-2

The

y

-intercept of

6

indicates that the line passes through

(0, 6)

. Substituting

(0, 6)

and

(4, -2)

into the slope formula yields

m = \frac{6 - (-2)}{0 - 4} = \frac{8}{-4} = -2

Identify the coordinates of two points on line

m

The line passes through

(4, -2)

and the

y

-intercept point

(0, 6)

The

y

-intercept is the point where

x = 0

Apply the slope formula

m = \frac{y_2 - y_1}{x_2 - x_1}

Substitute

(x_1, y_1) = (4, -2)

and

(x_2, y_2) = (0, 6)

into the formula:

m = \frac{6 - (-2)}{0 - 4}

Slope represents the ratio of vertical change to horizontal change between two points on a line.

Simplify the fractional expression.

m = \frac{8}{-4} = -2

Dividing positive

8

by negative

4

gives

-2

Slope of a line given two points or a point and intercept

Question