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 =  $- \frac{6}{5}$

 ⇒  y - 3 =  $- \frac{6}{5}$ ( x - (-5))
 ⇒  y - 3 =  $- \frac{6}{5}$ (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 = $- \frac{6}{5}$x + ($- \frac{6}{5}$ (5))
      y - 3 =  $- \frac{6}{5}$x - 6
           y =  $- \frac{6}{5}$x - 3

In the general form;
    y - 3 =  $- \frac{6}{5}$ (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 $- \frac{6}{5}$ is 
 y =  $- \frac{6}{5}$x - 3 (y-intercept form)  OR  5y + 6x = -15 (general form).