Question

What is the equation of the line that is parallel to the given line and has an x-intercept of –3?

Answer 1

(3,1)(0,-1)
slope = (-1 - 1) / (0 - 3) = -2/-3 = 2/3...a parallel line will have the same slope

y = mx + b
slope(m) = 2/3
(-3,0)...x = -3 and y = 0
now we sub and find b, the y int
0 = 2/3(-3) + b
0 = -2 = b
2 = b

so ur parallel equation is : y = 2/3x + 2

Answer 2

Answer:

$y = \frac{2}{3}x+2$

Step-by-step explanation:

Slope-intercept form:

The equation of line is given by:

y = mx+b           .....[1]

where

m is the slope of the line and

b is the y-intercept

Formula for slope:

$\text{Slope} = \frac{y_2-y_1}{x_2-x_1}$

For the graph we have;

Coordinates of the line are:

(3, 1) and (0, -1)

By slope formula we have;

$\text{Slope(m)} = \frac{-1-1}{0-3} = \frac{-2}{-3}=\frac{2}{3}$

It is also given that the x-intercept of line is, -3

⇒x-intercept = (-3, 0)

Substitute the given value in [1] we have;

$y = \frac{2}{3}x+b$

Substitute the point (-3, 0) we have;

$0= \frac{2}{3}(-3)+b$

⇒$0 = -2+b$

Add 2 to both sides we have;

b = 2

Then, our equation become:

$y = \frac{2}{3}x+2$ with positive slope 2/3 and y-intercept is 2

Therefore, the equation of the line that is parallel to the given line and has an x-intercept of –3 is:

$y = \frac{2}{3}x+2$