Using the point-gradient form y - y₁ = m ( x - x₁ )
y₁ = 3; x₁ = -5; m = [tex]- \frac{6}{5} [/tex]
⇒ y - 3 = [tex]- \frac{6}{5} [/tex] ( x - (-5))
⇒ y - 3 = [tex]- \frac{6}{5} [/tex] (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 = [tex]- \frac{6}{5} [/tex]x + ([tex]- \frac{6}{5} [/tex] (5))
y - 3 = [tex]- \frac{6}{5} [/tex]x - 6
y = [tex]- \frac{6}{5} [/tex]x - 3
In the general form;
y - 3 = [tex]- \frac{6}{5} [/tex] (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 [tex]- \frac{6}{5} [/tex] is
y = [tex]- \frac{6}{5} [/tex]x - 3 (y-intercept form) OR 5y + 6x = -15 (general form).
