Question

Find the equation of the line through (6,4) and (-3,-8)

Answer 1

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:

$\frac{y_2-y_1}{x_2-x_1}$

we will use (6,4) as $x_1[tex] and [tex]y_1$ and we will use (-3,-8) as $x_2[tex] and [tex]y_2$. we plug this into the slope formula:

$\frac{-8-4}{-3-6}$

-8 - 4 = -12

-3 - 6 = -9

the slope is $\frac{-12}{-9}$

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 $\frac{4}{3}$

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