Question

What is the equation of the line that passes through point (4,12) and has a y-intercept of -2?

Answer 1

Option B:

The equation of a line is $y=\frac{7}{2}x-2$.

Solution:

Given data:

Line passing through the point (4, 12).

y-intercept of the line = –2

The equation of a line in slope-intercept form is

y = mx + c

where m is the slope and c is the y-intercept.

c = –2

Substitute c = –2 in slope-intercept form.

y = mx – 2 – – – – (1)

To find m, substitute (4, 12) in the above equation.

12 = m(4) – 2

12 = 4m – 2

Add 2 on both sides of the equation.

14 = 4m

Divide by 2 on both sides of the equation.

$\frac{14}{4}=m$

$\frac{7}{2}=m$

Slope = $\frac{7}{2}$

Substitute m value in equation (1), we get

$y=\frac{7}{2}x-2$

The equation of a line is $y=\frac{7}{2}x-2$.

Hence Option B is the correct answer.