Question

What is the equation, in Ax+By=C form, of a line passing through (-4, -6) with a slope of 5/4?

a) 4x−5y=−14
b) 5x−4y=−24
c) 4x+5y=−14
d) 5x+4y=−24

Answer 1

The equation of the line passing through (-4, -6) with a slope of 5/4 in the form Ax + By = C is 5x - 4y = 4.

Step-by-step explanation:

To find the equation of a line in the form Ax + By = C, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

In this case, the point is (-4, -6) and the slope is 5/4.

Substituting these values into the equation gives us:

y - (-6) = (5/4)(x - (-4))

y + 6 = (5/4)(x + 4)

Next, we can multiply both sides of the equation by 4 to get rid of the fraction:

4y + 24 = 5(x + 4)

Expanding the right side gives us:

4y + 24 = 5x + 20

Now, we can rearrange the equation in the form Ax + By = C:

5x - 4y = 4

So, the correct answer is 5x - 4y = 4 (option b).