Couple things to note:
- Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
- Slope can be calculated using any two points on a line and the formula y₁ - y₂ / x₁ - x₂.
For the first problem, we know the slope of Function A is 6 (refer to slope-intercept form above). To compare the slopes of Function A and Function B, first find the slope of Function B.
Use y₁ - y₂ / x₁ - x₂. Two points on the line are (0, 1) and (-1, -2). Plug these into the formula accordingly and solve for slope.
y₁ - y₂ / x₁ - x₂
1 - (-2) / 0 - (-1)
1 + 2 / 0 + 1
3 / 1
3
The slope of Function B is 3. This is half of 6 (the slope of Function A), so the correct answer to question 1 is the first option: Slope of Function B = 2 × Slope of Function A.
For the second problem, substitute m and b in y = mx + b according to the graph. b is the y-intercept (the point at which the line intersects the y-axis); it is (0, -4), or -4. This gives us
y = mx - 4
We must now find m. Follow the same steps above to find slope. Our two points are (-2, 0) and (0, -4).
y₁ - y₂ / x₁ - x₂
0 - (-4) / -2 - 0
0 + 4 / -2
4 / -2
-2
Substitute.
y = -2x - 4
The first option is the correct answer.
Answer: The fabric costs $7.60 per yard.
Step-by-step explanation: First we can divide it by 106 then multiply it by 100 to get rid of the 6% sales tax, which now the cost of the stuff is $17.50.
Next, we subtract 8 from this to represent the clothing pattern cost. Now it is $9.50.
The last stap to this is to divide it by 1 1/4 to get the final cost per yard:
The fabric costs $7.60 per yard.
3/10=4/x
3x=10(4)
3x=40
x=13.33
Answer:
4x + 5 = 101
Step-by-step explanation:
<u>Step 1: Determine how much money both have</u>
Aylen: x
Rich: 5 + 3x
<u>Step 2: Write an equation and solve</u>
Aylen + Rich = 101
x + 5 + 3x = 101
<u>Step 3: Solve the equation</u>
x + 5 + 3x = 101
4x = 96
x = 24
Step 4: Determine how much money does Aylan and Rich have
Aylan has $24
Rich has 5 + 3(24) = $77
