Write an equation in slope-intercept form of the line that passes through the given points.(2,6)and (-4,-2) answer with all three steps

Step-by-step explanation:

They are asking for the equation Y = mX + b , of two given points

We need to find the slope and the interception of the points.

1) The slope of the line

We can use the point slope form, and clear for the slope m

y - y1 = m (x-x1)

m = (y -y1) / (x -x1)

The data given is: A (2, 6) and B (-4, -2)

Then the slope is: m = (6 -(-2)) / (2 -(-4)) = (6+2)/(2+4)=  8/6  = 4/3

2) Find the interception

From the general  equation slope intercept  Y = mX + b, clear b

b = Y - mX

Now substitute any given point to obtain b the interception

b = Y - mX

Lets choose point A (2, 6), remember m = 4/3

b = 6 - (4/3)(2)=10/3  

3) Therefore with the values of m and b, the general equation is:

Y = mX + b   -->  

Y = (4/3)X + 10/3  

its the fourth option

the image of (6, 9) under a dilation is (4, 6). the scale factor is