Question

Write the equation of the line that passes through the point M (-4;3) and is parallel to the line 5y–2x+ 6=0

Answer 1

Assuming the format is ay+bx+c=0

5y-2x-23=0

Explanation:

Equation 1: 5y - 2x + 6 = 0

Rearrange to form y=mx+c

5y = 2x - 6

By dividing by 5 we get

y = 0.4x - 1.2

Because the lines are parallel they share the same gradient.

Equation 2: 5y - 2x + c = 0

If we know that the line passes through x-coordinate (-4), and y-coordinate (3), we can substitute them in.

5(3) - 2(-4) + c = 0

Expanding Brackets

15+8+c=0 (Remember double negative = positive)

Rearranging this we get c = -23

Then we sub this back in to Equation 2 and we get 5y - 2x - 23 = 0.

Hope this helps!