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Y=-x+5 & y=-1/3x-1“Graph the lines and find the point of intersection”

User Tpdance
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1 Answer

3 votes

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

User Obskyr
by
8.3k points

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