Question

Which equation in slope-intercept form represents the line that passes through the points (−3, 7) and (4, 10)?

A.

y = 37x + 587y = 37x + 587

B.

y = 37x + 407y = 37x + 407

C.

y = 3x + 16y = 3x + 16

D.

y = 3x − 2y = 3x − 2

Answer 1

Which equation in slope-intercept form represents the line that passes through the points (−3, 7) and (4, 10)?

A.

y = 3/7x+58/7

B.

y = 3/7x + 40/7

C.

y = 3x + 16

D.

y = 3x − 2

Answer 2

why is it a

Answer 3

To determine the equation of the line that passes through the points \((-3, 7)\) and \((4, 10)\), we can follow these steps:

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the points \((-3, 7)\) and \((4, 10)\):
\[
m = \frac{10 - 7}{4 - (-3)} = \frac{3}{4 + 3} = \frac{3}{7}
\]

2. **Use the point-slope form** of the line equation, which is:
\[
y - y_1 = m(x - x_1)
\]
We can use either point. Let's use \((-3, 7)\):
\[
y - 7 = \frac{3}{7}(x + 3)
\]

3. **Distribute the slope**:
\[
y - 7 = \frac{3}{7}x + \frac{9}{7}
\]

4. **Add 7 to both sides (or \(\frac{49}{7}\)) to get y alone**:
\[
y = \frac{3}{7}x + \frac{9}{7} + \frac{49}{7}
\]
\[
y = \frac{3}{7}x + \frac{58}{7}
\]

This is in slope-intercept form \(y = mx + b\), with \(m = \frac{3}{7}\) and \(b = \frac{58}{7}\).

Now, let's check the options given:

A. \(y = 37x + 587\)
B. \(y = 37x + 407\)
C. \(y = 3x + 16\)
D. \(y = 3x - 2\)

None of those options perfectly match the calculated slope and y-intercept based on the provided points. It appears there might be a discrepancy or error in the answer choices. The slope was calculated as \( \frac{3}{7} \), but in simplified terms appears to align with the option representing 3; it may be evaluating a scaled form.

Upon verifying further,

Checking for \(m = 3\) the options can give \(3x + 16 = y\) or any matching.

Could you please clarify the values or ranges you wish to target?

Answer 4

To find the correct slope-intercept form equation that represents the line passing through the points \((-3, 7)\) and \((4, 10)\), let's go through the steps again to ensure we accurately derive the equation.

1. **Calculate the slope (m)**:

Using the formula for slope:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let \((x_1, y_1) = (-3, 7)\) and \((x_2, y_2) = (4, 10)\):
\[
m = \frac{10 - 7}{4 - (-3)} = \frac{3}{4 + 3} = \frac{3}{7}
\]

2. **Use the point-slope form of the line equation**:
Using the point-slope form:
\[
y - y_1 = m(x - x_1)
\]
Using the point \((-3, 7)\):
\[
y - 7 = \frac{3}{7}(x + 3)
\]

3. **Distributing the slope**:
\[
y - 7 = \frac{3}{7}x + \frac{9}{7}
\]

4. **Rearranging to slope-intercept form**:
Add \(7\) to both sides. Since \(7\) can be written as \(\frac{49}{7}\), we have:
\[
y = \frac{3}{7}x + \frac{9}{7} + \frac{49}{7}
\]
\[
y = \frac{3}{7}x + \frac{58}{7}
\]

Now we can compare this with the provided options:

A. \(y = \frac{3}{7}x + \frac{58}{7}\)
B. \(y = \frac{3}{7}x + \frac{40}{7}\)
C. \(y = 3x + 16\)
D. \(y = 3x - 2\)

The correct answer, based on our calculations, is:

**A. \(y = \frac{3}{7}x + \frac{58}{7}\)**.

This is the equation that represents the line passing through the given points.

Answer 5

Let's break down why option A is the correct answer for the line passing through the points \((-3, 7)\) and \((4, 10)\).

We previously calculated the equation step by step. Here's a recap of the process and why option A matches correctly.

1. **Finding the Slope**:
- Slope \( m \) is calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting in the points:
- For \((x_1, y_1) = (-3, 7)\) and \((x_2, y_2) = (4, 10)\):
\[
m = \frac{10 - 7}{4 - (-3)} = \frac{3}{7}
\]

2. **Using Point-Slope Form**:
- The point-slope form of a linear equation is:
\[
y - y_1 = m(x - x_1)
\]
Using the point \((-3, 7)\):
\[
y - 7 = \frac{3}{7}(x + 3)
\]

3. **Distributing the Slope**:
- Distributing gives:
\[
y - 7 = \frac{3}{7}x + \frac{3}{7} \cdot 3
\]
\[
y - 7 = \frac{3}{7}x + \frac{9}{7}
\]

4. **Rearranging into Slope-Intercept Form**:
- We need to isolate y:
\[
y = \frac{3}{7}x + \frac{9}{7} + 7
\]
- Recognizing that \(7 = \frac{49}{7}\):
\[
y = \frac{3}{7}x + \frac{9}{7} + \frac{49}{7}
\]
\[
y = \frac{3}{7}x + \frac{58}{7}
\]

Now, let's analyze the options provided:

- **A. \(y = \frac{3}{7}x + \frac{58}{7}\)**: This matches our derived equation precisely with slope \(\frac{3}{7}\) and y-intercept \(\frac{58}{7}\).

- **B. \(y = \frac{3}{7}x + \frac{40}{7}\)**: This has the correct slope but an incorrect y-intercept.

- **C. \(y = 3x + 16\)**: The slope of \(3\) is not correct and does not match our calculated slope.

- **D. \(y = 3x - 2\)**: Similar to option C, the slope is incorrect.

### Conclusion:
The only option that accurately represents the line through the points \((-3, 7)\) and \((4, 10)\) with the correct slope and y-intercept is **A**. Thus, option A is correct.