Question

Write the equation of a line in slope intercept form that passes through the two points. (-1,3) and (2,9)

Answer 1

Answer:

$y = 2x +5$

Step-by-step explanation:

Finding the Slope:

m = rise/run

$m=\frac{9-3}{2-(-1)}=\frac{6}{3}=\boxed{2}$

The slope is 2.

Finding the y-intercept:

$y = 2x + b\\\\9 = 2(2) + b\\\\9 = 4 + b\\\\9 - 4 = 4 - 4 + b\\\\\boxed{ 5 = b}$

The y-intercept is (0,5).

The equation should be: $y = 2x +5$.

Hope this helps.

Answer 2

Answer:

y = 2x+5

Step-by-step explanation:

To find the equation in slope intercept form, we first have to find the slope of the two points.

The formula for finding the slope is:

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

We are given the points:

(-1, 3) and (2, 9)

x1, y1 and x2, y2.

$\frac{9-3}{2-(-1)}$

$\frac{6}{3}$ or 2 (the slope).

The slope intercept form is written as:

y= mx + b

y=2x+b

To find b, we can plug in either of the points given. Personally, I like to work with positive numbers. I'll be using the point (2, 9), however, either point will get you to the same answer.

y=2x+b

9=2(2)+b

9=4+b

Now subtract 4 from both sides.

5=b

Which then leaves us with the equation:

y = 2x+5