Question

Hi, I am struggling massively. I keep getting outrageous fractions when trying to solve the one with the equation for a line. For the points of intersection, I do not know how to interpret it. I will be eternally grateful if you please help me! Thank you in advance.

Answer 1

The first step is to find the slope

m= (y2-y1)/(x2-x1)

Notice the negative negative which is a positive

=( 13/14 - 31/16)/ (5/7 - 5/8)

m = -113/10

2nd problem

y = x^2 y = 18x - x^2

Set them equal

x^2 = 18x-x^2

Add x^2 to each side

2x^2 = 18x

Subtract 18x

2x^2 -18x = 0

Factor out 2x

2x( x-9) =0

Using the zero product property

2x=0 x-9 =0

x=0 x=9

When x = 0 y=0

When x = 9 y = 9^2 = 81

We have 2 points so we can make a line

(0,0) and ( 9,81)

m = ( 81-0)/(9-0) = 9

Y intercept is 0

y = mx+b

y = 9x +0

y = 9x