Question

Which is an equation in slope intercept form of the line that passes through (2, 16) and (-1, 7)?​

Answer 1

Answer:

y = 3x + 10

Step-by-step explanation:

We are given that a line has the points (2, 16), and (-1, 7)

We want to write the equation of this 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, hence its name

First, we need to find the slope of the line
The slope 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 calculate the slope

$x_1=2\\y_1=16\\x_2=-1\\y_2=7$

Now substitute into the formula (m is the slope)

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

m=$\frac{7-16}{-1-2}$

Subtract

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

Divide

m=3

The slope of the line is 3.

Here is the equation of our line so far:

y=3x+b

Now we need to find b

As the equation passes through the points (2,16) and (-1, 7), we can use either one of them to solve for b.

Taking (2,16) for example:

Substitute 2 as x and 16 as y.

16 = 3(2) + b

Multiply

16 = 6 + b

Subtract 6 from both sides

10 = b

Substitute 10 as b in the equation

y = 3x + 10

Topic: writing the equation of the line

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