Question

what is the equation of a line that is parallel to -3x + 4y = 4 and passes through the point (4, 0) ?​

Answer 1

y=3x4-3

Explanation:

find the equation of the line parallel to the line −3x+4y=4 passing through the point (4,0).

The equation of the line in the slope-intercept form is y=3x4+1.

The slope of the parallel line is the same: m=34.

So, the equation of the parallel line is y=3x4+a.

To find a, we use the fact that the line should pass through the given point: 0=(34)⋅(4)+a.

Thus, a=−3.

Therefore, the equation of the line is y=3x4−3.

Answer: y=3x4−3.

Answer 2

`y = (3)/(4)x - 1`

Explanation:

Parallel lines have equal gradients.

Therefore, the equation -3x + 4y = 4 will be expressed as follows in the form

`y = mx + c`

where m = gradient

c = y-intercept

4y = 3x + 4

`y = (3)/(4)x + 1`

from the equation, the gradient =
`(3)/(4)`

the equation should pass through the line with point (x , y) and (4 , 0) and have the gradient of 3/4

This means that:

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

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

`y = (3)/(4)x -1`