How do you explain why two graphed lines have the same slopes but different y -intercepts?(1 point) Responses The lines are intersecting. The lines are intersecting. The lines are parallel. The lines are parallel. The lines overlap completely. The lines overlap completely. Not enough information is given.

Question

GPT-4o mini · Answer

The correct response is: **The lines are parallel.** When two lines have the same slope but different y-intercepts, it means that they will run alongside each other without ever intersecting. This is a characteristic of parallel lines in a Cartesian coordinate system.

...hi.... · Answer

A line has an equation of y=−x+6 . What are the slope and y -intercept?(1 point) Responses The slope is −1, and the y-intercept is 6. The slope is negative 1 , and the y -intercept is 6. The slope is 6, and the y-intercept is −1. The slope is 6, and the y -intercept is negative 1 . The slope is 1, and the y-intercept is 6. The slope is 1, and the y -intercept is 6. There is no slope, and the y-intercept is 6. There is no slope, and the y -intercept is 6.

GPT-4o mini · Answer

The correct response is: **The slope is −1, and the y-intercept is 6.** In the equation $ y = -x + 6 $, the coefficient of $ x $ gives the slope, which is $ -1 $, and the constant term provides the y-intercept, which is $ 6 $.

...hi.... · Answer

Use the image and table to answer the question. McIntosh Apples ($) Cost per Pound Pounds ($) Cost 2 3.70 3 5.55 4 7.40 The costs per pound for Granny Smith apples and McIntosh apples are displayed in the graph and table. Which type of apple is cheaper per pound, and what is the cost per pound? (1 point) Responses Granny Smith apples are cheaper at $1.75 per pound. Granny Smith apples are cheaper at $1.75 per pound. McIntosh apples are cheaper at $1.75 per pound. McIntosh apples are cheaper at $1.75 per pound. McIntosh apples are cheaper at $1.85 per pound. McIntosh apples are cheaper at $1.85 per pound. Granny Smith apples are cheaper at $1.85 per pound. Granny Smith apples are cheaper at $1.85 per pound. Skip to navigation

GPT-4o mini · Answer

To determine which type of apple is cheaper per pound, we need to look at the cost per pound for both McIntosh apples (provided in the table) and the cost per pound for Granny Smith apples (which is not included in your message but can be checked in the graph you mentioned).

Based on the information provided for McIntosh apples:

For 2 pounds, the cost is $3.70, so the cost per pound is $ \frac{3.70}{2} = 1.85$.
For 3 pounds, the cost is $5.55, so the cost per pound is $ \frac{5.55}{3} \approx 1.85$.
For 4 pounds, the cost is $7.40, so the cost per pound is $ \frac{7.40}{4} = 1.85$.

The cost per pound for McIntosh apples is consistently $1.85.

To determine which type of apple is cheaper, you would need the cost per pound for Granny Smith apples to compare. However, based on your provided answer options, the one that references McIntosh apples appears to be relevant. If you find that Granny Smith apples have a higher price per pound than $1.85, then McIntosh would be cheaper.

If you have the cost per pound for Granny Smith apples, please share it for an accurate comparison. If we assume from your options that this cost is higher, then:

The correct response would be: McIntosh apples are cheaper at $1.85 per pound.

...hi.... · Answer

Use the image to answer the question. Using the graph, derive the equation of the line in slope-intercept form. (1 point) Responses y=3x+4 y equals 3 x plus 4 3x−y=4 3 x minus y equals 4 y=3x−4 y equals 3 x minus 4 y=−3x−4 y equals negative 3 x minus 4 Skip to navigation

GPT-4o mini · Answer

To derive the equation of the line in slope-intercept form ($y = mx + b$), you need to determine the slope ($m$) and the y-intercept ($b$) from the graph you're referring to.

Slope (m): The slope can be found by identifying two points on the line and calculating the rise over run (change in y over change in x).
Y-Intercept (b): This is the point where the line crosses the y-axis, which is the value of $y$ when $x=0$.

Given the answer choices you've provided, we can make some deductions about the possible equations:

If the slope is positive and the line rises from left to right, then the slope $m$ would be positive.
If the line has a slope of $3$ and intercepts the y-axis at $4$, then the equation would be $y = 3x + 4$.
A slope of $3$ with a negative y-intercept would give $y = 3x - 4$.

Without the specific details from the graph, here are the possible interpretations based on the answer choices:

If the line rises and crosses the y-axis above zero: $y = 3x + 4$
If it rises and crosses the y-axis below zero: $y = 3x - 4$
If it has a negative slope (falls as you move from left to right), then it could be represented as $y = -3x - 4$.

To provide the most accurate answer, please confirm what the graph indicates about the slope and intercept. Based on typical cases without that visual reference, you might use the most common positive slope case given in the options: $y = 3x + 4$.

...hi.... · Answer

Use the image to answer the question. Write the equation of the line in slope-intercept form. (1 point) Responses y=−5x+1 y equals negative 5 x plus 1 −5x−y=−1 negative 5 x minus y equals negative 1 y=5x+1 y equals 5 x plus 1 y=−5x−1 y equals negative 5 x minus 1 Skip to navigation

GPT-4o mini · Answer

To write the equation of the line in slope-intercept form ($y = mx + b$), you need to know the slope ($m$) and the y-intercept ($b$). Here's how to interpret the options you've provided:

Determine the Slope and Y-Intercept from the Graph:
- The slope is the steepness of the line (how much it rises or falls for a unit increase in $x$).
- The y-intercept is the point where the line crosses the y-axis (where $x = 0$).

Based on the provided options:

If the slope is negative and the y-intercept is $1$, the equation would be $y = -5x + 1$.
If the slope is negative and the y-intercept is $-1$, then the equation would be $y = -5x - 1$.
If the slope is positive $5$ and the y-intercept is $1$, then the equation would be $y = 5x + 1$.

Without viewing the graph:

If the slope is $-5$ (which indicates a steep negative slope), you would check the y-intercept:
- If it crosses at $1$, choose $y = -5x + 1$.
- If it crosses at $-1$, choose $y = -5x - 1$.

If the slope is $5$, choose $y = 5x + 1$.

If you have seen the graph, choose the option that matches the slope and the y-intercept derived from the graph. If $-5$ is indeed the slope and you see an intercept of $1$, for example, select:

$y = -5x + 1$.

Please adjust your answer based on the actual slope and intercept you see on the graph!

...hi.... · Answer

Use the image to answer the question. Is this the correct graph of y=−13x+4?(1 point) Responses Yes, it is the correct graph because this graph has a y-intercept of (0,3). Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 3 right parenthesis . Yes, it is the correct graph because this graph has a y-intercept of (0,4). Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 4 right parenthesis . No, it is not the correct graph because this graph used (0,3) as the y-intercept. No, it is not the correct graph because this graph used left parenthesis 0 comma 3 right parenthesis as the y -intercept. No, it is not the correct graph because this graph has a positive slope. No, it is not the correct graph because this graph has a positive slope. Skip to navigation

GPT-4o mini · Answer

To determine if the provided graph is the correct graph for the equation $y = -13x + 4$, we need to analyze the features of this equation:

Y-Intercept: The y-intercept of this equation is $4$, which means that the graph should cross the y-axis at the point $(0, 4)$.
Slope: The slope of this line is $-13$, meaning the line has a steep negative slope, indicating that as $x$ increases, $y$ decreases significantly.

Based on the options provided:

If the graph shows a y-intercept at $(0, 3)$, then the graph is not correct, as the y-intercept should be at $(0, 4)$.
If the graph correctly shows the y-intercept at $(0, 4)$, then it may be the correct graph depending on the slope.

Given these details, the correct responses would be:

Yes, it is the correct graph because this graph has a y-intercept of (0, 4). (Only if the graph correctly shows the y-intercept at that point)
No, it is not the correct graph because this graph used (0, 3) as the y-intercept. (If the graph shows the y-intercept at $(0, 3)$)

Additionally, if the graph has a positive slope, it cannot be a correct representation of $y = -13x + 4$, which has a negative slope.

Thus:

If the graph has a y-intercept at (0, 4) and a negative slope: Yes, it is the correct graph because this graph has a y-intercept of (0, 4).
If the graph instead has (0, 3) or displays a positive slope: No, it is not the correct graph because this graph used (0, 3) as the y-intercept, or has a positive slope.