Question

A line passes through (- 1, 1) and (3,9).

Answer 1

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 $\frac{y_2-y_1}{x_2-x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points

Let's label the values of the points before we start, to avoid confusion and mistakes

$x_1 = -1\\y_1=1\\x_2=3\\y_2=9$

Now substitute into the formula (note: the formula has SUBTRACTION, and we have NEGATIVE numbers, so we'll end up subtracting a negative)

m = $\frac{y_2-y_1}{x_2-x_1}$

m = $\frac{9-1}{3--1}$

Simplify

m=$\frac{9-1}{3+1}$

m=$\frac{8}{4}$

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

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