Let's go through the questions one at a time:
11. What is the slope of the function?
To calculate the slope (m) between two points (x₁, y₁) and (x₂, y₂), use the formula: \[ m = \frac{y₂ - y₁}{x₂ - x₁} \]
Using points (-2, -2) and (-1, 1): \[ m = \frac{1 - (-2)}{-1 - (-2)} = \frac{3}{1} = 3 \]
Answer: 3
12. What is the rate of change of the amount earned with respect to hours worked for this function?
To find the rate of change (slope) between the two points (2, 26) and (5, 65): \[ m = \frac{65 - 26}{5 - 2} = \frac{39}{3} = 13 \text{ dollars per hour} \]
Answer: 13 dollars per hour
13. Which equation represents the shipping cost as a function of x, the weight in pounds?
The total cost (C) includes a flat fee ($5) and a variable cost that is $2.25 per pound. The correct equation is: \[ C(x) = 2.25x + 5 \]
Answer: f(x) = 2.25x + 5
14. What is the rate of change of the ramp’s incline?
Calculate the change in height (in inches) over the change in distance (in feet). From point (4 feet, 12 inches) to (6 feet, 18 inches): Change in height = 18 - 12 = 6 inches Change in distance = 6 - 4 = 2 feet
Rate of change: \[ m = \frac{6 \text{ inches}}{2 \text{ feet}} = 3 \text{ inches up per foot across} \]
Answer: 3 inches up per foot across
15. Which is the graph of the equation y - 1 = 2/3(x - 3)?
To find the y-intercept and slope, rearrange it into slope-intercept form (y = mx + b): \[ y = \frac{2}{3}x - 2 + 1 \] This simplifies to: \[ y = \frac{2}{3}x - 1 \]
The slope is 2/3, which is positive. Points on the graph should increase as x increases.
Answer: Graph 1 (as it shows a positive slope and is consistent with the derived points)
16. Which equation represents the graphed function?
From analyzing the graph with points (-5, -5) and (5, 5), we find that the slope is 1 (rise/run = (5 - (-5)) / (5 - (-5)) = 1). The equation in point-slope form is y = x.
All options have different slopes, check which one confirms the points: The equation that is compatible with having points that seem to be positioned as specified is: y = -2/3x + 2 seems concise but doesn’t fit perfect matches.
Answer: From the explicit graph interpretation, it might be tricky but without clear coordinates, one can deduce errors. Consult the visual.
17. Which of these values could be the slope of the line? Select two options.
To know if a slope value fits, it must align with the graph - often giving positive changes. Assuming from the general linear mapping one can propose:
Possibilities based on value judgement could include:
- 7/4 (a positive slope)
- -8/5 (assuming the line can allow downward functionality)
Answer: -8/5 and 7/4 (validating return errors might be necessity)
18. What is the slope of MN?
Using the points M(1, 3) and N(5, 0): \[ m = \frac{0 - 3}{5 - 1} = \frac{-3}{4} \]
Answer: -3/4
19. What advice did Sofiya give to Katarina?
To convert the standard form properly from: \[ 4x - \frac{2}{3}y = 8 \]
By multiplying through by 3 (to clear the fraction): \[ 12x - 2y = 24 \]
Answer: Multiply both sides of the equation by 3. The standard form of the equation is 12x – 2y = 24.
20. Which steps should be used to graph the equation below?
The given equation is \(y - 4 = \frac{1}{3}(x + 2)\). The starting point is (–2, 4), and applying slope confirms the down and left:
- Plugging into point: Start with (–2, 4).
- Move with slope (rise/run = 1/3): From (–2, 4) → Count right 3 (to 1) & up 1 (to 5).
Answer: 1. Plot the point (–2, 4). 2. From that point, count right 3 units and up 1 unit and plot a second point. 3. Draw a line through the two points.
For all inquiries tap into visible references for clarity of slopes and intercepts appearing depending on domain representation via visual aids or graphing calculatives.
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