The table below shows corresponding values of x and y for a linear relationship in the sta… — ACT

The table below shows corresponding values of $x$ and $y$ for a linear relationship in the standard $(x, y)$ coordinate plane.

$x$	$y$
$-3$	$13$
$1$	$5$
$5$	$a$
$b$	$-7$

What is the value of $a + b$ ?

4Answer
B
8
C
-8
D
28
E
-2

Answer

The correct answer is

4

. The slope of the line is determined to be

-2

using the points

(-3, 13)

and

(1, 5)

. This gives the equation of the line as

y = -2x + 7

. Substituting

x = 5

yields

a = -3

, and substituting

y = -7

yields

b = 7

. Adding these values together gives

4

Step-by-Step Solution

Calculate the slope of the linear relationship using the points

(-3, 13)

and

(1, 5)

Slope

m = -2

Since the relationship is linear, the slope is constant and is given by

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

Determine the equation of the line using the point-slope formula with point

(1, 5)

and slope

-2

Equation is

y = -2x + 7

Using

y - y_1 = m(x - x_1)

allows us to find the relation between any

x

and

y

coordinate on this line.

Find the value of

a

by substituting

x = 5

into the linear equation.

a = -3

The table indicates that when

x = 5

, the

y

-value is

a

Find the value of

b

by substituting

y = -7

into the linear equation and solving for

x

b = 7

The table indicates that when

y = -7

, the

x

-value is

b

Sum the values of

a

and

b

a + b = 4

The question asks for the sum

a + b

Key Concept

Linear Equations and Graphing

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

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