The graph of a linear function is shown in the xy-plane. The line passes through the point… — SAT

The graph of a linear function is shown in the $xy$ -plane. The line passes through the points $(-2, -3)$ and $(2, 5)$ . If the point $(k, 11)$ lies on the line, what is the value of $k$ ?

A
9
B
14
5Answer
D
6

Answer

The slope of the line is calculated as

m = \frac{5 - (-3)}{2 - (-2)} = 2

. Using the point-slope form with the point

(2, 5)

, the equation of the line is

y - 5 = 2(x - 2)

, which simplifies to

y = 2x + 1

. Substituting the point

(k, 11)

into this equation gives

11 = 2k + 1

, which solves to

k = 5

Step-by-Step Solution

Calculate the slope of the line using the points

(-2, -3)

and

(2, 5)

m = 2

The slope formula is

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

. Substituting the given coordinates:

m = \frac{5 - (-3)}{2 - (-2)} = \frac{8}{4} = 2

Determine the equation of the line using point-slope form

y = 2x + 1

Using

y - y_1 = m(x - x_1)

with the point

(2, 5)

and

m = 2

, we get

y - 5 = 2(x - 2)

, which simplifies to

y = 2x + 1

Substitute

(k, 11)

into the line equation and solve for

k

k = 5

Substituting

x = k

and

y = 11

yields

11 = 2k + 1

. Subtracting 1 from both sides gives

10 = 2k

, and dividing by 2 gives

k = 5

Key Concept

Finding the linear equation from coordinates and solving for variables

Question

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