Question

Write the slope-intercept form of an equation of the line that passes through (2,-4) and (0,6)

Answer 1

Hey there!

In order to write the slope-intercept form, we have to have slope, and the y intercepts, just as it says in the name. In order to find slope with two points, we use our formula:

y2-y1/x2-x1 =
6-(-4)/0-2 = 6+4/-2 =
10/-2 = -5

Now that we know our slope is negative five, we can use one of those poins to model our slope intercept form, y= mx+b, using our slope, to solve for b, our y intercepts. We'll use (0,6).

We have:

6 = -2(0) + b
6 = 0 + b
6 = b

Now, since we have the slope and y intercept, we can write the equation:

y = -2x + 6

Hope this helps!

Answer 2

we know that

the equation of the line in the slope-intercept form is equal to

$y=mx+b$

where

m is the slope of the line

b is the y-intercept of the line

Let

$A(2,-4)\\B(0,6)$

Step $1$

Find the slope of the line AB

the slope between two pints is equal to

$m=\frac{(y2-y1)}{(x2-x1)}$

substitute the values

$mAB=\frac{(6+4)}{(0-2)}$

$mAB=\frac{(10)}{(-2)}$

$mAB=-5$

with the slope m and the point B find the value of b

$B(0,6)$

$6=-5*0+b$

$b=6$

Find the equation of the line

$y=mx+b$

$y=-5x+6$

therefore

the answer is

$y=-5x+6$