In the standard (x, y) coordinate plane, a line passes through the points (3, -1) and (-1,… — ACT

In the standard $(x, y)$ coordinate plane, a line passes through the points $(3, -1)$ and $(-1, y)$ . If the slope of the line is $-2$ , what is the value of $y$ ?

A
$1$
B
$-9$
C
$-7$
$7$ Answer
E
$9$

Answer

The correct value of

y

7

To find the value of

y

, apply the slope formula

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

. Substituting the coordinates

(3, -1)

and

(-1, y)

alongside the slope of

-2

yields the equation

-2 = \frac{y - (-1)}{-1 - 3}

. Simplifying the denominator gives

-2 = \frac{y + 1}{-4}

. Multiplying both sides of the equation by

-4

results in

8 = y + 1

. Finally, subtracting

1

from both sides gives

y = 7

Step-by-Step Solution

Set up the slope formula using the given points

(x_1, y_1) = (3, -1)

and

(x_2, y_2) = (-1, y)

The formula is

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

, which becomes

-2 = \frac{y - (-1)}{-1 - 3}

This establishes the algebraic relationship between the coordinates and the given slope.

Simplify the numerator and denominator of the fraction.

-2 = \frac{y + 1}{-4}

Subtracting a negative number is equivalent to addition, and

-1 - 3

simplifies to

-4

Solve for

y

by isolating the variable.

Multiply both sides by

-4

to get

8 = y + 1

, then subtract

1

from both sides to get

y = 7

This isolates the variable

y

to find its numerical value.

Key Concept

Calculating the slope of a line using the coordinates of two points on the line.

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