Equation of line passes through (2,4), (5,13)

Hey there! :) 

To find the equation of a line that passes through (2, -4) & (5, 13), we must first find the slope.

To find the slope, we must use the slope equation, which is : m = (y₂-y₁) / (x₂-x₁)

So, let's plug everything in! 

m = (y₂ - y₁) / (x₂ - x₁)

m = (13 - (-4)) / (5 - 2)

Simplify.

m = (13 + 4) / 3

Simplify.

m = 17/3

So, our slope is 17/3! 

Now, let's find the equation of the line using slope-intercept form.

Remember that slope-intercept form is : y=mx+b where m=slope, b=y-intercept.

Since we already have the slope, all we need to do is find the y-intercept.

To find the y-intercept, let's plug all of our known variables into y-intercept form, using the points (2, 4) and the slope 17/3.

y = mx + b

(4) = (17/3)(2) + b

Simplify.

4 = 24/3 + b

Simplify.

4 = 8 + b

Subtract 8 from both sides.

4 - 8 = b

Simplify.

-4 = b

So, our y-intercept is b! 

Using our known variables (slope, y-intercept), we can very easily plug it into a new slope-intercept equation! 

y = mx + b

So, since our slope is 17/3 and our y-intercept is -4, let's plug and chug! 

y = 17/3x - 4 → our final answer

~Hope I helped!~