Answer:
1. D
2. F
3. F
4. C
5. F
6. B
Step-by-step explanation:
1. To find the slope, take two points from the table (in this case I'll use points (-3, 7) and (-1, 4)) and put them into the expression: [tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{4-7}{-1-(-3)}[/tex]
Solve:
4 - 7 = -3
-1 - (-3) = -1 + 3 = 2
The slope is -[tex]\frac{3}{2}[/tex]
2. I used the same process I used in number 1 using the points (-2, 4) and
(1, -1)
3. The slope of both equations represents how much each t-shirt was sold for. This means that whichever equation has a higher slope made greater profits. The slope of store B is 3.75 - we know this because the equation given is in y = mx, where m is the slope. To find the slope of store A, use the method I used in question 1 using two points from the graph ( I used points (0, 0) and (10, 40)). The slope of store A is 4, which is greater than 3.75, meaning that Store A made a greater profit per t-shirt.
4. To find the slope and y-intercept of this equation, let's convert the equation to slope-intercept form, y= mx + b, where m is the slope and b is the y-intercept. To do this we have to isolate the y:
y + 9x = -6
Subtract 9x from both sides to isolate the y:
y + 9x - 9x = -6 - 9x
y = -6 - 9x
This equation can also be written as: y = -9x - 6
Now we can see that the slope is -9 and the y-intercept is -6.
5. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Slope is also known as rise over run. Looking the graph, for every 2 points it decreases on the y-axis, it increases by 1 on the x-axis. This can be written as -2/1, or simply -2. To find the y-intercept, find the point on the graph where the line intersects the y-axis. In this case, it's at y = -1. Now that we know the values of our slope and y-intercept, we can put them into the equation:
y = mx + b
y = -2x - 1
6. The y-intercept represents the amount Alice will have to pay for the game center before she pays for any guests. This value is $100.
