Answer:
y = 2x + 3
Step-by-step explanation:
Hi there!
We are given the points (-1, 1) and (3,9) which belong to a line
We want to write the equation of the line in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
First, let's find the slope of the line
The slope (m) can be found using the formula
, where
and
are points
Let's label the values of the points before we start, to avoid confusion and mistakes
![x_1 = -1\\y_1=1\\x_2=3\\y_2=9](https://tex.z-dn.net/?f=x_1%20%3D%20-1%5C%5Cy_1%3D1%5C%5Cx_2%3D3%5C%5Cy_2%3D9)
Now substitute into the formula (note: the formula has SUBTRACTION, and we have NEGATIVE numbers, so we'll end up subtracting a negative)
m = ![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
m = ![\frac{9-1}{3--1}](https://tex.z-dn.net/?f=%5Cfrac%7B9-1%7D%7B3--1%7D)
Simplify
m=![\frac{9-1}{3+1}](https://tex.z-dn.net/?f=%5Cfrac%7B9-1%7D%7B3%2B1%7D)
m=![\frac{8}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B4%7D)
Divide
m = 2
The slope of the line is 2
We can substitute this as m in y=mx+b.
y = 2x + b
Now we need to find b
As the equation passes through the point (-1, 1) and (3, 9), we can use either point to help solve for b.
Taking (3, 9) for example:
substitute 3 as x and 9 as y.
9 = 2(3) + b
Multiply
9 = 6 + b
Subtract 6 from both sides
3 = b
Substitute 3 as b in the equation
y = 2x + 3
Hope this helps!
Topic: finding the equation of the line
See more on this topic here: brainly.com/question/27645483