Question

Find the slope between the two points given. Then, use the slope and one of the points to write the equation of the line in Slope-Intercept form. State the slope and y-intercept.

Answer 1

Equation: y=2x-1

Slope: 2

y-intercept: -1

Explanation:

Hi there!

We are given the points (-1, -3) and (-2, -5). We need to find the slope, equation of the line, and the y intercept of the line

First, let's find the slope

The formula for the slope (m) 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 we need for the formula, but let's label the values of the points to avoid any confusion

x1=-1

y1=-3

x2=-2

y2=-5

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

m=
`(-5--3)/(-2--1)`

simplify

m=
`(-5+3)/(-2+1)`

add

m=
`(-2)/(-1)`

divide

m=2

So the slope is 2

Now let's find the equation of the line

The question asks for it to be in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

We calculated the slope from earlier, so let's substitute that into the equation

y=2x+b

Now we need to find b

The equation will pass through both (-1, -3) and (-2, -5) so we can use either one of them to solve for b (doesn't matter which one)

Let's take (-1, -3) as an example

substitute -1 as x and -3 as y into the equation

-3=2(-1)+b

multiply

-3=-2+b

Add 2 to both sides

-1=b (the value of the y intercept!)

Substitute -1 as b into the equation

y=2x-1

We found everything needed for this problem

Hope this helps!