Question

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

Answer 1

y = 2x+5

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:

`(y2-y1)/(x2-x1)`

We are given the points:

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

x1, y1 and x2, y2.

`(9-3)/(2-(-1))`

`(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

Answer 2

`y = 2x +5`

Explanation:

Finding the Slope:

m = rise/run

`m=(9-3)/(2-(-1))=(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.