Find the slope & the intercept P1(3, -4) & P2(-3, 4)

Question

Intermediate Algebra

Answer 1

Slope is change in y over change in x. Look at the two points;

 

P₁ has a y-value of  -4

P₂ has a y-value of +4

 

The change in y is 8 units!  Think: what's the difference between -4 and +4?

 

Or, thing what's the distance on the number line between -4 and +4?

 

P1 has a x-value of +3
P2 has a x-value of  -3

 

Likewise, The change in x is the difference between 3 and -3 so the  The change in x is 6 units!

 

 

The slope is 8/6 .....  reduces to 4/3   Leave the slope as an improper fraction (you will see why later on)

Answer 2

Hi Shelby,

 

To find the slope you can use the slope formula

 

m = (y₁ - y₂)/(x₁ - x₂)

. . . which means slope ("m") equals "y" minus "y" divided by "x" minus "x"

 

m = (-4 - 4)/[3 - (-3)]

m = (-8)/(3 + 3)

m = -8/6

m = -4/3

 

Now that you have the slope, you can use the "slope-intercept" form of a linear equation to find the y-intercept (which is the place where the line connecting your two points crosses the y-axis).

 

y = mx + b

(m = slope, b = y-intercept) . . . we can use either of the coordinates as our "x" and "y" values.

 

-4 = (-4/3) * 3 + b

-4 = -12/3 + b

-4 = -4 + b

0 = b