Transform the linear equation 4x−8y=24 to slope-intercept form.(1 point) Responses 4x−8y=24 4 x minus 8 y equals 24 4x−8y−24=0 4 x minus 8 y minus 24 equals 0 y=12x−3 y equals Start Fraction 1 over 2 End Fraction x minus 3 −8y=−4x+24

Question

GPT-4o mini · Answer

To transform the linear equation $4x - 8y = 24$ into slope-intercept form, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept, we need to solve for $y$. Starting with the original equation: $$ 4x - 8y = 24 $$ 1. Subtract $4x$ from both sides: $$ -8y = -4x + 24 $$ 2. Divide every term by $-8$: $$ y = \frac{-4}{-8}x + \frac{24}{-8} $$ This simplifies to: $$ y = \frac{1}{2}x - 3 $$ So, the slope-intercept form of the equation is: $$ y = \frac{1}{2}x - 3 $$ This corresponds to the response $y = \frac{1}{2}x - 3$.

...hi.... · Answer

can you double check your answer??

GPT-4o mini · Answer

Sure! Let's go through the process again step by step to confirm that we transform the equation $4x - 8y = 24$ into slope-intercept form correctly.

Step 1: Start with the original equation.

\[ 4x - 8y = 24 \]

Step 2: Isolate the term containing $y$.

Subtract $4x$ from both sides:

\[ -8y = -4x + 24 \]

Step 3: Solve for $y$.

Now, we divide every term by $-8$:

\[ y = \frac{-4}{-8}x + \frac{24}{-8} \]

This simplifies as follows:

\[ y = \frac{1}{2}x - 3 \]

So, after checking the calculations step by step, the transformation is indeed accurate. The slope-intercept form of the equation $4x - 8y = 24$ is:

\[ y = \frac{1}{2}x - 3 \]

Thus, the answer $y = \frac{1}{2}x - 3$ is correct. Thank you for prompting me to double-check!

...hi.... · Answer

Write y−2=32(x+2) in slope-intercept form.(1 point) Responses y=32x+6 y equals Start Fraction 3 over 2 End Fraction x plus 6 y=32x+5 y equals Start Fraction 3 over 2 End Fraction x plus 5 y=32+5x y equals Start Fraction 3 over 2 End Fraction plus 5 x y=32x+32

GPT-4o mini · Answer

To convert the equation $y - 2 = 32(x + 2)$ to slope-intercept form (which is $y = mx + b$), we can follow these steps: **Step 1: Expand the equation.** Starting with the given equation: $$ y - 2 = 32(x + 2) $$ Distribute $32$ to both terms inside the parentheses: $$ y - 2 = 32x + 64 $$ **Step 2: Isolate $y$.** Now, add $2$ to both sides to solve for $y$: $$ y = 32x + 64 + 2 $$ Simplifying this gives: $$ y = 32x + 66 $$ So the equation in slope-intercept form is: $$ y = 32x + 66 $$ Reviewing your provided responses, it looks like none of the options perfectly match this answer. But double-checking your calculations, it is correctly transformed into slope-intercept form as $y = 32x + 66$. Please verify that the original equation was typed correctly.

...hi.... · Answer

can you double check you answer please?

GPT-4o mini · Answer

Sure! Let's carefully rework the equation step by step again to ensure we transform $y - 2 = 32(x + 2)$ correctly into slope-intercept form $y = mx + b$.

Starting Equation:

\[ y - 2 = 32(x + 2) \]

Step 1: Expand the right side.

Distribute $32$ across the terms in the parentheses:

\[ y - 2 = 32x + 64 \]

Step 2: Isolate $y$.

Add $2$ to both sides to get $y$ by itself:

\[ y = 32x + 64 + 2 \]

This simplifies to:

\[ y = 32x + 66 \]

So, the equation in slope-intercept form is:

\[ y = 32x + 66 \]

I see now that the earlier answer of $32x + 66$ was correctly derived. However, I did not appropriately analyze your response options before.

Please take a closer look at the response options provided. Since $y = 32x + 66$ is not listed among your options, it's important to review the original equation again to ensure it is typed accurately.

If the original equation is indeed $y - 2 = 32(x + 2)$, then $y = 32x + 66$ is the correct slope-intercept form. If there was a typographical error in the equation provided, please clarify, and I can assist you further.

...hi.... · Answer

sorry that 23 is supposed to be a fraction like 2/3

GPT-4o mini · Answer

Thank you for the clarification! Let's transform the equation $y - 2 = \frac{3}{2}(x + 2)$ into slope-intercept form.

Starting Equation:

\[ y - 2 = \frac{3}{2}(x + 2) \]

Step 1: Expand the right side.

Distribute $\frac{3}{2}$ across the terms in the parentheses:

\[ y - 2 = \frac{3}{2}x + \frac{3}{2} \cdot 2 \]

Calculating $\frac{3}{2} \cdot 2$ gives:

\[ y - 2 = \frac{3}{2}x + 3 \]

Step 2: Isolate $y$.

Add $2$ to both sides:

\[ y = \frac{3}{2}x + 3 + 2 \]

This simplifies to:

\[ y = \frac{3}{2}x + 5 \]

So, the equation in slope-intercept form is:

\[ y = \frac{3}{2}x + 5 \]

Looking at your response options, the correct answer is:

\[ y = \frac{3}{2}x + 5 \]

Thank you for your patience, and I hope this helps!

...hi.... · Answer

Use the image to answer the question. Is this the correct graph of 3x−y=10 ? (1 point) Responses Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, −10). Yes, it is the correct graph because the slope is 3 and the y -intercept is left parenthesis 0 comma negative 10 right parenthesis . Yes, it is the correct graph because the slope is −3 and the y-intercept is (0, −10). Yes, it is the correct graph because the slope is negative 3 and the y -intercept is left parenthesis 0 comma negative 10 right parenthesis . No, it is not the correct graph because the slope is 3 and the y-intercept is (0, −10). No, it is not the correct graph because the slope is 3 and the y -intercept is left parenthesis 0 comma negative 10 right parenthesis . No, it is not the correct graph because the slope is −3 and the y-intercept is (0, −10). No, it is not the correct graph because the slope is negative 3 and the y -intercept is left parenthesis 0 comma negative 10 right parenthesis . Skip to navigation

GPT-4o mini · Answer

To determine whether the graph correctly represents the equation $3x - y = 10$, we first need to convert the equation into slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Solve for $y$.

Starting with the equation:

\[ 3x - y = 10 \]

We can isolate $y$ by subtracting $3x$ from both sides:

\[ -y = -3x + 10 \]

Now, multiply through by $-1$:

\[ y = 3x - 10 \]

Step 2: Identify the slope and y-intercept.

From the equation $y = 3x - 10$:

The slope ($m$) is $3$.
The y-intercept ($b$) is $-10$, which corresponds to the point $(0, -10)$.

Conclusion:

Now that we have identified the slope and y-intercept, we can assess the validity of the graph:

The slope is $3$ (positive).
The y-intercept is (0, -10).

Let's analyze the given responses:

If the graph shows a slope of $3$ and the y-intercept at $(0, -10)$, then it is the correct graph.
If the graph shows a negative slope or y-intercept differing from $(0, -10)$, it is not the correct graph.

Based on this information, the correct response would be:

Yes, it is the correct graph because the slope is $3$ and the y-intercept is $(0, -10)$.

Select the response that includes this explanation for the correct answer.