Question

Find the equation of the line through points (-5,-6) and (4,12)

Answer 1

y=2x+4

Explanation:

Hi there!

We want to find the equation of the line that passes through the points (-5, -6) and (4, 12)

The most common way to write the equation of the line is in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

First, let's find the slope of the line

The formula for the slope calculated from two points is
`(y_2-y_1)/(x_2-x_1)`, where (
`x_1`,
`y_1`) and (
`x_2`,
`y_2`) are points

We have everything needed to calculate the slope, but let's label the values of the points to avoid any confusion

`x_1`=-5

`y_1`=-6

`x_2`=4

`y_2`=12

Now substitute into the formula (remember: the formula has SUBTRACTION in it)

m=
`(y_2-y_1)/(x_2-x_1)`

m=
`(12--6)/(4--5)`

Simplify

m=
`(12+6)/(4+5)`

Add

m=
`(18)/(9)`

Divide

m=2

So the slope of the line is 2

Here is the equation so far:

y=2x+b

We need to find b

As the line will pass through both (-5, -6) and (4, 12), we can use the values of either one to solve for b

Let's take (4, 12) for instance

Substitute 4 as x and 12 as y

12=2(4)+b

Multiply

12=8+b

Subtract 8 from both sides

4=b

Substitute 4 as b in the equation

y=2x+4

Hope this helps!

Answer 2

9514 1404 393

Answer:

y = 2x +4

Explanation:

The slope can be found using the slope formula:

m = (y2 -y1)/(x2 -x1)

m = (12 -(-6))/(4 -(-5)) = 18/9 = 2

The y-intercept can be found from ...

b = y -mx

b = 12 -(2)(4) = 4

Then the slope-intercept equation for the line is ...

y = mx +b

y = 2x +4