A line in the standard (x, y) coordinate plane has a y-intercept that is 4 units greater t… — ACT

A line in the standard $(x, y)$ coordinate plane has a $y$ -intercept that is $4$ units greater than its slope. If the line passes through the point $(5, -2)$ , what is the $y$ -intercept of the line?

Answer: 3

Answer

The correct answer is 3.

The

y

-intercept is found by setting up the equation using the given point and the relationship between the slope and the

y

-intercept, yielding

b = 3

Step-by-Step Solution

Define the relationship between the slope

m

and the

y

-intercept

b

m = b - 4

The problem states the

y

-intercept is

4

units greater than the slope, so

b = m + 4

Substitute the point

(5, -2)

and the slope expression into the slope-intercept equation

y = mx + b

-2 = (b - 4)(5) + b

The line passes through the point

(5, -2)

, so its coordinates must satisfy the line's equation.

Solve the algebraic equation for

b

b = 3

Expanding and simplifying the equation yields

-2 = 6b - 20

, which gives

6b = 18

, and dividing by

6

results in

b = 3

Key Concept

Linear Equations and Graphing

Question

Answer

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