The slope of a line is 2, and the line passes through the point (3, 1). What is the y-inte… — ACT

The slope of a line is $2$ , and the line passes through the point $(3, 1)$ . What is the $y$ -intercept of this line in the standard $(x,y)$ coordinate plane?

$-5$ Answer
B
$-4$
C
$1$
D
$2.5$
E
$5$

Answer

The

y

-intercept of the line is

-5

The correct answer is found by substituting the slope

m = 2

and the point

(3, 1)

into the slope-intercept equation

y = mx + b

. This gives

1 = 2(3) + b

, which simplifies to

1 = 6 + b

. Subtracting

6

from both sides isolates

b

, giving

b = -5

Step-by-Step Solution

Recall the slope-intercept form of a linear equation.

y = mx + b

, where

m

is the slope and

b

is the

y

-intercept.

This formula allows us to solve for the

y

-intercept using the given slope and a point on the line.

Substitute the given slope

m = 2

and the coordinates of the point

(3, 1)

into the slope-intercept equation.

1 = 2(3) + b

The point

(3, 1)

lies on the line, so its coordinates must satisfy the equation of the line.

Simplify the equation and solve for

b

1 = 6 + b \Rightarrow b = -5

Subtracting

6

from both sides isolates

b

, which represents the

y

-intercept of the line.

Key Concept

Linear Equations and Graphing

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