Question

Use the point-slope formula to write an equation of the line that passes through (-5,3) and

Answer 1

Answer:

The equation in point slope form is $y-6=\frac{1}{3}(x-4)$

The equation in slope intercept form is $y=\frac{1}{3}x-\frac{14}{3}$

Step-by-step explanation:

step 1

Find the slope m

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$(-5,3),(4,6)$

Substitute the values

$m=\frac{6-3}{4+5}$

$m=\frac{3}{9}$

simplify

$m=\frac{1}{3}$

step 2

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{1}{3}$

$(4,6)$

substitute

$y-6=\frac{1}{3}(x-4)$ ---> equation in point slope form

step 3

Find the equation of the line in slope intercept form

$y=mx+b$

$y-6=\frac{1}{3}(x-4)$ ----> convert to slope intercept form

$y-6=\frac{1}{3}x-\frac{4}{3}$

$y=\frac{1}{3}x-\frac{4}{3}+6$

$y=\frac{1}{3}x-\frac{14}{3}$