In the standard (x,y) coordinate plane, a line has an x-intercept of (a, 0), where a \neq … — ACT

In the standard $(x,y)$ coordinate plane, a line has an $x$ -intercept of $(a, 0)$ , where $a \neq 0$ , and a $y$ -intercept of $(0, 2a)$ . If the line passes through the point $(4, -3)$ , what is the value of $a$ ?

Answer: 2.5

Answer

The value of

a

2.5

Representing the intercepts as

(a, 0)

and

(0, 2a)

lets us find the slope of the line, which is

m = \frac{2a - 0}{0 - a} = -2

. The line can then be written as

y = -2x + 2a

. Substituting the point

(4, -3)

into the equation yields

-3 = -2(4) + 2a

, which simplifies to

2a = 5

, and therefore

a = 2.5

Step-by-Step Solution

Find the slope of the line in terms of the variable

a

The slope is

m = -2

Applying the slope formula to the points

(a, 0)

and

(0, 2a)

yields

m = \frac{2a - 0}{0 - a} = -2

Write the general equation of the line.

The equation is

y = -2x + 2a

The slope is

-2

and the

y

-intercept is

2a

, so the equation in slope-intercept form is

y = mx + b

Substitute the coordinates of the point

(4, -3)

to find

a

a = 2.5

Substituting

x = 4

and

y = -3

into

y = -2x + 2a

gives

-3 = -8 + 2a

, which simplifies to

2a = 5

and

a = 2.5

Key Concept

Linear Equations and Graphing

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic