Question

. Write the equation of a line with a slope of 4 passing through the point (3, 1). Write the

equation in slope-intercept form.

Answer 1

The answer is:

y = 4x - 11

Work/explanation:

First, we will write the equation in point slope:

`\sf{y-y_1=m(x-x_1)}`

where m = slope;

(x₁,y₁) is a point on the line.

Plug in the data:

`\sf{y-1=4(x-3)}`

Simplify

`\sf{y-1=4x-12}`

Add 1 on each side

`\sf{y=4x-12+1}`

`\sf{y=4x-11}`

Hence, the equation is y = 4x - 11.

Answer 2

y = 4x - 11

Explanation:

The general equation of the slope-intercept form of a line is given by:

y = mx + b, where

• (x, y) are any point on the line,
• m is the slope,
• and b is the y-intercept.

We can find b, the y-intercept of the line, by plugging in 4 for m and (3, 1) for (x, y) in the slope-intercept form:

1 = 4(3) + b

1 = 12 + b

-11 = b

Thus, the y-intercept is -11.

Thus, the equation of the line with a slope of 4 passing through the point (3, 1) in slope-intercept form is y = 4x - 11