Question

Find an equation for the line parallel to 4 y + 24 x = 32 and goes through the point ( 1 , − 4 ) . Write your answer in the form y = m x + b .

Answer 1

Answer: y = - 6x + 2

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

4y + 24x = 32

Rearranging it so that it will take the slope intercept form, it becomes

4y = - 24x + 32

Dividing through by 4, it becomes

y = - 6x + 8

Comparing with the slope intercept form, slope = - 6

If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (1,-4) is - 6

To determine the intercept, we would substitute m = - 6, x = 1 and y = -4 into y = mx + c. It becomes

- 4 = - 6 × 1 + c = - 6 + c

c = - 4 + 6 = 2

The equation becomes

y = - 6x + 2