A line graphed in the standard (x,y) coordinate plane has an x-intercept of 6 and a y-inte… — ACT

A line graphed in the standard $(x,y)$ coordinate plane has an $x$ -intercept of $6$ and a $y$ -intercept of $-3$ . What is the slope of this line?

Answer: 0.5

The slope of the line is

0.5

(or

\frac{1}{2}

The correct slope is

0.5

. By identifying the

x

-intercept as

(6, 0)

and the

y

-intercept as

(0, -3)

, we can apply the slope formula

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

to find

m = \frac{-3 - 0}{0 - 6} = \frac{-3}{-6} = 0.5

Identify the coordinates of the intercepts on the coordinate plane.

The points are

(6, 0)

and

(0, -3)

x

-intercept of

6

means the line crosses the

x

-axis at

(6, 0)

. A

y

-intercept of

-3

means the line crosses the

y

-axis at

(0, -3)

Apply the slope formula with the identified coordinates.

m = \frac{-3 - 0}{0 - 6} = \frac{-3}{-6} = 0.5

The slope formula is defined as

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

for any two points on a line.

Calculating the slope of a line from its intercepts

Question