A line in the standard (x,y) coordinate plane passes through the point (0, 4) and has a sl… — ACT

A line in the standard $(x,y)$ coordinate plane passes through the point $(0, 4)$ and has a slope of $3$ . Which of the following equations represents this line?

$y = 3x + 4$ Answer
B
$y = 4x + 3$
C
$y = 3x - 4$
D
$y = -3x + 4$
E
$y = \frac{1}{3}x + 4$

Answer

y = 3x + 4

The slope-intercept form of a linear equation is

y = mx + b

. Here, the slope

m

is given as

3

, and the y-intercept

b

is given as

4

since the line crosses the y-axis at the point

(0,4)

. Substituting these values into the form gives the equation

y = 3x + 4

Step-by-Step Solution

Identify the slope-intercept form of a linear equation.

The slope-intercept form is

y = mx + b

, where

m

is the slope and

b

is the

y

-intercept.

To write the equation of a line, we can substitute the known slope and y-intercept into this general form.

Determine the values of

m

and

b

from the given information.

The slope

m = 3

. The point

(0, 4)

lies on the y-axis, meaning the y-intercept

b = 4

The y-intercept is the y-coordinate of the point where the line crosses the y-axis, which occurs when

x = 0

Substitute the values of

m

and

b

into the slope-intercept equation.

y = 3x + 4

Replacing

m

with

3

and

b

with

4

yields the equation representing the line.

Key Concept

Writing linear equations in slope-intercept form using the slope and a point.

Question

Answer

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