HW 4 review

1) Find the slope of the following

a) GRAPH
^Rise/_run = ^{DOWN 4}/_{right 5} = ^-4/₅
b) (5, 10) and (1, 2)
m = ^(y-y)/_(x-x) = ^(10-2)/_(5-1) = ⁸/₄ = 2

c) (-3, 5) and (12, -5)
m = ^(y-y)/(x-x) = ^{(5 - -5)} / _{(-3 - 12)} = ¹⁰/_-15 = ^-2/₃

2) Find the equation of the line that has a slope of m = 4 and goes through the point (2, 10)

First we plug in m, x, and y to solve for b:
y = mx + b
10 = 4(2) + b
10 = 8 + b
-8 | -8
2 = b

So now we know m = 4 and b = 2 so we can write our equation!
y = 4x + 2

3) Given the equations below, put all into slope intercept form

a) 5x + 5y = 20
- 5x | - 5x
5y = 20 - 5x
5 | 5 5
y = 4 - 1y

​b) -10x + 2y = 8
+ 10x | + 10x
2y = 8 + 10x
2 | 2 2
y = 4 + 5x

​c) 3x - 4y = 16
- 3x | -3x
-4y = 16 - 3x
-4 | -4 -4
y = -4 + ³/₄x

4) Is the point (2, 10) a solution to the equation y = 4x + 2?

Explain your answer!

y = 4x + 2
10 = 4(2) + 2
10 = 8 + 2
10 = 10
YES!

​We substitute the point (2, 10) into the equations. Then we solve and see that it is the same on both sides so it IS a solution!

5) Is the point (-4, 5) a solution to the equation y = 3x + 7?

Explain your answer!

y = 3x + 7
5 = 3(-4) + 7
5 = -12 + 7
5 = -5
NO!

​We substitute the point (-4, 5) into the equations. Then we solve and see that it is NOT the same on both sides so it is NOT a solution!

6) Is the point (3, 2) a solution to the equation 2x + 4y = 12?

Explain your answer!

2x + 4y = 12
2(3) + 4(2) = 12
6 + 8 = 12
14 = 12
NO

​We substitute the point (3, 2) into the equations. Then we solve and see that it is NOT the same on both sides so it is NOT a solution!