Question

Find an equation for the line with the given property. (a) It passes through the point (2, −6) and is parallel to the line 4x + y − 10 = 0.

It has x-intercept 6 and y-intercept 4.

Answer 1

`y = -4x + 2`

Explanation:

Required

Determine the equation

From the question, we understand that, it is parallel to:

`4x + y -10 = 0`

This means that they have the same slope.

Make y the subject to calculate the slope of:
`4x + y -10 = 0`

`y = -4x + 10`

The slope of a line with equation
`y =mx + c` is m

By comparison:

`m = -4`

So, the slope of the required equation is -4.

The equation is then calculated as:

`y = m(x - x_1) + y_1`

Where:

`(x_1.y_1) = (2,-6)`

So, we have:

`y = -4(x - 2) -6`

Open bracket

`y = -4x + 8 -6`

`y = -4x + 2`