Question

A line includes the points (12, 13) and (6, 8). What is its equation in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

y = 5/6x + 3

Explanation:

Slope intercept form : y = mx + b

Where m = slope and b = y intercept

Step 1 Find the slope

We can find the slope using the slope formula

Slope = (y1 - y2) / (x1 - x2)

Where the values of x and y derive from known points (x1,y1) and (x2,y2)

Here the points are (12,13) and (6,8)

So we have (x1,y1) = (12,13) and (x2,y2) = (6,8)

This means that x1 = 12 , y1 = 13 , x2 = 6 and y2 = 8

Again, Slope = (y1 - y2) / (x1 - x2)

==> plug in x1 = 12, y1 = 13, x2 = 6, y2 = 8

Slope(m) = (13-8)/(12-6)

==> simply subtraction

Slope(m) = 5/6

So m = 5/6

We can plug that into slope form and we get

y = 5/6x + b

Step 2 find y intercept

Now to find b or the y intercept, we can plug in one of the given points and solve for b

y = 5/6x + b

(x,y) = (6,8) so x = 6 and y = 8

8 = 5/6(6) + b

==> multiply 5/6 and 6

8 = 5 + b

==> subtract 5 from both sides

3 = b

So the y intercept is at (0,3) and b = 3

Now we plug that into slope intercept form

And as a result we get y = 5/6x + 3

For more validation refer to the attached image.