Answer:
y = 4/3x - 4
Step-by-step explanation:
to find the equation of a line with 2 points, we use the slope formula which is:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
we will use (6,4) as [tex]x_1[tex] and [tex]y_1[/tex] and we will use (-3,-8) as [tex]x_2[tex] and [tex]y_2[/tex]. we plug this into the slope formula:
[tex]\frac{-8-4}{-3-6}[/tex]
-8 - 4 = -12
-3 - 6 = -9
the slope is [tex]\frac{-12}{-9}[/tex]
but we can simplify this further by dividing the fraction by -3
-12 / -3 = 4
-9 / -3 = 3
the simplified version of the slope is [tex]\frac{4}{3}[/tex]
we can write this in slope-intercept form which is y =mx + b, with b being the y intercept and m being the slope
y = 4/3x + b <--- we need to solve for b in order to find the y intercept, so substitute x & y for a point on the line, we can use any point we are given, but for this example i will use (6,4)
4 = 4/3(6) + b < multiply 4/3 x 6
4 = 8 + b < subtract 8 from both sides
-4 = b
our y intercept would be (0,-4)
the equation looks like the following:
y = 4/3x - 4, which is our answer
