Question

Given a line whose slope is, m, is -6/5, and passes through point (-5,3), the graph will?

Answer 1

Using the point-gradient form y - y₁ = m ( x - x₁ )
y₁ = 3; x₁ = -5; m =
`- (6)/(5)`

⇒ y - 3 =
`- (6)/(5)` ( x - (-5))
⇒ y - 3 =
`- (6)/(5)` (x + 5)

Now, you can approach here in two ways: put it in the y-intercept form or the general form.

In the y-intercept form;
y - 3 =
`- (6)/(5)`x + (
`- (6)/(5)` (5))
y - 3 =
`- (6)/(5)`x - 6
y =
`- (6)/(5)`x - 3

In the general form;
y - 3 =
`- (6)/(5)` (x + 5)
by multiplying through by 5
⇒ 5 ( y - 3 ) = -6 ( x + 5)
⇒ 5y - 15 = -6x - 30
⇒ 5y + 6x = -15

∴ the line that passes through (-5, 3), with gradient
`- (6)/(5)` is
y =
`- (6)/(5)`x - 3 (y-intercept form) OR 5y + 6x = -15 (general form).