Question

Rewrite the equation in slope-intercept form.
Show each step!

-2x + y = 1

Answer 1

Rewrite the equation in slope-intercept form.
Show each step!

y - 4 = -3(x - 3)

Answer 2

Question: Find the point-slope equation of the line with slope -3 that passes through the point (2,-10).
Solution:
y - y1 = m(x - x1)
y - (2) = -3(x - (-10))
y - 2 = -3(x + 10)
The equation of the line is y - 2 = -3(x + 10)
What is the error? Explain how to solve the problem.

Answer 3

To rewrite the equation \(-2x + y = 1\) in slope-intercept form, which is given by the formula \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y-intercept), follow these steps:

1. **Start with the original equation:**
\[
-2x + y = 1
\]

2. **Isolate \(y\) on one side of the equation.** To do this, we need to add \(2x\) to both sides of the equation:
\[
y = 2x + 1
\]

Now, the equation is in slope-intercept form:

- The slope \(m\) is \(2\).
- The y-intercept \(b\) is \(1\).

Thus, the slope-intercept form of the equation \(-2x + y = 1\) is:
\[
y = 2x + 1
\]

Answer 4

To rewrite the equation \(y - 4 = -3(x - 3)\) in slope-intercept form \(y = mx + b\), follow these steps:

1. **Start with the given equation:**
\[
y - 4 = -3(x - 3)
\]

2. **Distribute \(-3\) on the right side:**
\[
y - 4 = -3x + 9
\]

3. **Add \(4\) to both sides to solve for \(y\):**
\[
y = -3x + 9 + 4
\]

4. **Simplify the right side:**
\[
y = -3x + 13
\]

Now, the equation is in slope-intercept form:

- The slope \(m\) is \(-3\).
- The y-intercept \(b\) is \(13\).

Thus, the slope-intercept form of the equation \(y - 4 = -3(x - 3)\) is:
\[
y = -3x + 13
\]

Answer 5

Let's identify the error in the provided solution for finding the point-slope equation of a line with a slope of \(-3\) that passes through the point \((2, -10)\).

The point-slope form of the equation of a line is:

\[
y - y_1 = m(x - x_1)
\]

Where:
- \((x_1, y_1)\) is a point on the line (in this case, \((2, -10)\)),
- \(m\) is the slope of the line.

### Given Data:
- Slope \(m = -3\)
- Point \((x_1, y_1) = (2, -10)\)

### Correct Application:

1. **Identify \(x_1\) and \(y_1\):**
- \(x_1 = 2\)
- \(y_1 = -10\)

2. **Plug these values into the point-slope form:**
\[
y - (-10) = -3(x - 2)
\]

3. **Simplify:**
\[
y + 10 = -3(x - 2)
\]

This simplifies the equation correctly, making it clear that it starts with \(y + 10\).

### Mistake in the Solution:
In the original solution, they incorrectly substituted \(y_1\) as \(2\) instead of \(-10\) and used \(-10\) incorrectly in the expression. The correct substitution should involve \(y_1 = -10\).

### Final Equation:
So the correct point-slope equation here is:
\[
y + 10 = -3(x - 2)
\]

You can also leave it as:
\[
y + 10 = -3(x - 2)
\]
or rearrange it further if necessary.

If re-arranged into slope-intercept form for clarity:
1. Distributing the right side:
\[
y + 10 = -3x + 6
\]

2. Subtract \(10\) from both sides:
\[
y = -3x - 4
\]

This final equation is in slope-intercept form, confirming the slope remains \(-3\) and passing through the point \((2, -10)\).