Question

Write the equation of a line, in slope-intercept form
(1,1);(-2,-11)
Y =

Answer 1

Y =4X -3

Explanation:

x1 y1 x2 y2

1 1 -2 -11

(Y2-Y1) (-11)-(1)= -12 ΔY -12

(X2-X1) (-2)-(1)= -3 ΔX -3

slope= 4

B= -3

Y =4X -3

Answer 2

y=4x-3

Explanation:

Hi there!

We are given the points (1,1) and (-2, -11) and we want to write the equation of the line in slop-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

So 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 we need to calculate the slope, let's just label the points to avoid confusion

`x_1=1\\y_1=1\\x_2=-2\\y_2=-11`

Now substitute those values into the formula

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

m=
`(-11-1)/(-2-1)`

Subtract

m=
`(-12)/(-3)`

Divide

m=4

So the slope of the line is 4

Here is the equation of the line so far:

y=4x+b

We need to find b

As the equation passes through both (1,1) and (-2, -11), we can plug either one of them into the equation to solve for b

Taking (1,1) will give us this:

1=4(1)+b

Multiply

1=4+b

Subtract 4 from both sides

-3=b

Substitute -3 as b into the equation

y=4x-3

Hope this helps!