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

Answer:

$y = -4x + 2$

Step-by-step 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

$y = -4x + 8 -6$

$y = -4x + 2$