Question

Write an equation for a line that is parallel to y + 5 = 3(x - 1) and goes through the point (3,-4)

Answer 1

The equation for a line that is parallel to y + 5 = 3(x - 1) and goes through the point (3,-4) will be:

• y = 3x-13

Explanation:

Given the equation

y + 5 = 3(x - 1)

Writing in the slope-intercept form

y=mx+b

where m is the slope and b is the y-intercept

y = 3(x-1) -5

y = 3x-3-5

y = 3x - 8

Thus, the slope = m = 3

We know that the parallel lines have equal slopes.

So, the slope of a parallel line is also 3

Using the point-slope form of the line equation

`y-y_1=m\left(x-x_1\right)`

substituting the values m = 3 and the point (3, -4)

y-(-4)=3(x-3)

y+4 = 3x-9

y = 3x-9-4

y = 3x-13

Thus, the equation for a line that is parallel to y + 5 = 3(x - 1) and goes through the point (3,-4) will be:

• y = 3x-13