Answer:
1) y = -8/5x + 8
2) slope = -3
3) x = 4
4) x ≥ 22/3
5) x = 21/16
6) x = 12
Step-by-step explanation:
1) For the slope, you know you go up 8 left 5 to get from the x-intercept to your y-intercept so it’s positive 8 over -5 (rise over run).
This makes your slope 8/-5 which is the same as -8/5
2) The slope is next to the x, so the slope is -3/1 which is -3.
3) Rearrange the equation to y = mx + b.
Firstly, subtract 6x from both sides:
-3y = -6x + 24
Then, divide both sides by -3:
y = 2x - 8
To get the x-intercept, divide the y-intercept (but positive) by the slope.
8/2 = 4
Your x-intercept is 4.
4) Distribute on the terms:
-53 ≥ -9x - 9 + 3x
Combine like terms:
-53 ≥ -6x - 9
Add 9 to both sides:
-44 ≥ -6x
Divide both sides by -6:
44/6 ≤ x
(Inequality flipped because you divide by a negative)
Simplify:
22/3 ≤ x
Flip the inequality:
x ≥ 22/3
5) Multiply both sides by 4:
3x - x/3 = 7/2
Multiply both sides by 3:
9x - x = 21/2
Combine like terms:
8x = 21/2
Divide both sides by 8:
x = 21/16
or
x = 1.3125
6) Combine like terms:
7x + 6 = 90
Subtract 6 from both sides:
7x = 84
Divide both sides by 7:
x = 12
Hope this helps!
