Answer:
[tex]\bf y =\dfrac{1}{3}x[/tex]
Step-by-step explanation:
(12,4) ⇒ x₁ = 12 & y₁ = 4
(-9,-3) ⇒ x₂ = -9 & y₂ = -3
Using the given points, find the slope.
[tex]\boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{-3-4}{-9-12}\\\\\\=\dfrac{-7}{-21}\\\\\\=\dfrac{1}{3}[/tex]
Equation of line in slope-intercept form:
y = mx + b
Here, m is the slope and b is the y-intercept.
[tex]\sf y = \dfrac{1}{3}x + b[/tex]
The line is passing through (12,4). Substituting the x and y co-ordinates, we get the value of 'b'.
[tex]\sf ~~~~~~~ 4 = \dfrac{1}{3}*12+b\\\\\\ ~~~~~~~~ 4 = 4 + b\\\\~~~4 - 4 = b\\[/tex]
b = 0
Now, the equation becomes,
[tex]\sf y =\dfrac{1}{3}x[/tex]
