Question

Convert the equation to slope-intercept form. You must show ALL work to earn full credit.
6x+2y=10

Answer 1

Write the equation of the line in slope-intercept form that goes through the points (-4, -6) and (3, 8). You must show ALL work to earn full credit.

Answer 2

Write the equation in slope-intercept form that has slope of 1 and goes through the point (2, -2). You must show ALL work to earn full credit.

Answer 3

To convert the equation \( 6x + 2y = 10 \) into slope-intercept form, which is given by the equation \( y = mx + b \) (where \( m \) is the slope and \( b \) is the y-intercept), follow these steps:

1. **Start with the original equation:**
\[
6x + 2y = 10
\]

2. **Isolate the \( y \) term.** To do this, subtract \( 6x \) from both sides of the equation:
\[
2y = 10 - 6x
\]

3. **Simplify the equation.** You can rewrite the right side:
\[
2y = -6x + 10
\]

4. **Divide every term by 2 to solve for \( y \):**
\[
y = \frac{-6}{2}x + \frac{10}{2}
\]

5. **Perform the division:**
\[
y = -3x + 5
\]

Now, the equation \( y = -3x + 5 \) is in slope-intercept form, where:
- The slope \( m = -3 \)
- The y-intercept \( b = 5 \)

Thus, the final answer is:
\[
y = -3x + 5
\]

Answer 4

To write the equation of the line in slope-intercept form that goes through the points \((-4, -6)\) and \((3, 8)\), we need to follow these steps:

1. **Find the slope (m)** using the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \((x_1, y_1) = (-4, -6)\) and \((x_2, y_2) = (3, 8)\).

Plugging in the coordinates:
\[
m = \frac{8 - (-6)}{3 - (-4)} = \frac{8 + 6}{3 + 4} = \frac{14}{7} = 2
\]

2. **Use the slope-intercept form equation, \(y = mx + b\)**, where \(m\) is the slope we found. We now have:
\[
y = 2x + b
\]

3. **Find the y-intercept (b)** by substituting one of the points into the equation. We'll use the point \((-4, -6)\):
\[
-6 = 2(-4) + b
\]

Simplifying this:
\[
-6 = -8 + b
\]
\[
b = -6 + 8
\]
\[
b = 2
\]

4. **Write the equation** using the slope and y-intercept:
\[
y = 2x + 2
\]

Thus, the equation of the line in slope-intercept form that goes through the points \((-4, -6)\) and \((3, 8)\) is:
\[
\boxed{y = 2x + 2}
\]

Answer 5

To write the equation of a line in slope-intercept form that has a slope of \(1\) and passes through the point \((2, -2)\), we will use the slope-intercept form of a line, which is given by:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept.

### Steps:

1. **Substitute the slope into the equation**:
Here, the slope \(m\) is \(1\):
\[
y = 1x + b \quad \text{or simply} \quad y = x + b
\]

2. **Use the given point to find \(b\)**:
We will plug in the coordinates of the point \((2, -2)\) into the equation to solve for \(b\):
\[
-2 = 1(2) + b
\]

Simplifying this:
\[
-2 = 2 + b
\]

Now, subtract \(2\) from both sides:
\[
-2 - 2 = b
\]
\[
-4 = b
\]

3. **Write the final equation**:
Now that we know \(b\), we can write the complete equation:
\[
y = x - 4
\]

Thus, the equation of the line in slope-intercept form that has a slope of \(1\) and goes through the point \((2, -2)\) is:
\[
\boxed{y = x - 4}
\]