In the standard (x,y) coordinate plane, a line is defined by the equation 3x - 2y = 12. Wh… — ACT

In the standard $(x,y)$ coordinate plane, a line is defined by the equation $3x - 2y = 12$ . What is the sum of the $x$ -intercept and the $y$ -intercept of this line?

-2Answer
B
10
C
2
D
16
E
1

Answer

The sum of the

x

-intercept and the

y

-intercept of the line is

-2

To find the

x

-intercept, set

y = 0

in the equation

3x - 2y = 12

, which gives

3x = 12

, so

x = 4

. To find the

y

-intercept, set

x = 0

, which gives

-2y = 12

, so

y = -6

. Adding these two values together gives

4 + (-6) = -2

Step-by-Step Solution

Find the

x

-intercept by setting

y = 0

in the equation.

Substitute

y = 0

into

3x - 2y = 12

to get

3x - 2(0) = 12

, which simplifies to

3x = 12

, yielding

x = 4

The

x

-intercept of a line is the point where the line crosses the

x

-axis, which occurs when the

y

-coordinate is

0

Find the

y

-intercept by setting

x = 0

in the equation.

Substitute

x = 0

into

3x - 2y = 12

to get

3(0) - 2y = 12

, which simplifies to

-2y = 12

, yielding

y = -6

The

y

-intercept of a line is the point where the line crosses the

y

-axis, which occurs when the

x

-coordinate is

0

Add the

x

-intercept and

y

-intercept together.

Calculate

4 + (-6) = -2

The question asks for the sum of the

x

-intercept and the

y

-intercept.

Key Concept

Finding the

x

- and

y

-intercepts of a linear equation in standard form.

Estimated Time:1m 0s

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Key Concept

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