The first equation is
y = -x + 5
second equation is
y = -1/3x - 1
Let us take this equation one after the other
for the first equation
y = -x + 5
we need to isolate one of the variables in order to get the other variable
to get x let make y = 0
substitute y = 0 into y = -x + 5
0 = -x +5
0 + x = 5
x = 5
to get y make x = 0
y = -(0) + 5
y = 0 + 5
y = 5
the first equation has (5, 5)
same process applies to the second equation
since y = -1/3x -1
let make x = 0 to get y
y = -1/3(0) - 1
y = 0 - 1
y = -1
to get x make y = 0
0 = -1/3x -1
0 = -1*x/3 -1
0 = -x/3 -1
our lowest common multiple is 3
0 = -x -3/3
introducing cross multiply
0 *3 = -x - 3
0 = -x -3
-x = 3
x = -3
the second equation has a point of (-3, -1)
our points are (5,5) and (-3,-1)
Using y = mx + c
slope = y2 - y1/x2 - x1
x1 = 5, y1 = 5, x2 = -3 and y2= -1
slope = -1 - 5/-3 -5
slope = -6/-8
slope = 3/4
to find the equation
y - 5 = 3/4 ( x - 5)
y - 5 = 3x - 15 /4
cross multiplication
4(y-5) = 3x - 15
4y - 20 = 3x -15
4y = 3x -15 +20
4y = 3x + 5
divide through by 4
y = 3/4x +5/4
the graph intersect at 5/4 or 1.25y = 3x -15