Question

use the graph to answer the question. write the equation of the line shown in the graph in slope-intercept form. (1 point) the equation in slope-intercept form is y=blank fractionx+blank

Answer 1

(-2,1)
(2,3)

Answer 2

To write the equation of a line in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, we need two key details about the line:

1. **The Slope** (\(m\)): This is found by determining how much \(y\) increases or decreases as \(x\) increases. It can be calculated using two points on the line: \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

2. **The Y-Intercept** (\(b\)): This is the point where the line crosses the y-axis, which can be directly read from the graph.

Without the visual of the graph, I can't tell you the exact values, but here’s how you would set it up:

1. Identify two points on the line. For example, say one point is (1, 2) and another point is (3, 4).

2. Calculate the slope:
\[
m = \frac{4 - 2}{3 - 1} = \frac{2}{2} = 1
\]

3. Find the y-intercept. Suppose the line crosses the y-axis at (0, 1), then \(b = 1\).

4. Substitute these values into the slope-intercept form:
\[
y = 1x + 1 \quad \text{or simplified} \quad y = x + 1.
\]

Your final answer will depend on the specific points on the graph. For example, if you found the slope as \( \frac{1}{2} \) and y-intercept as 3, the equation would be:
\[
y = \frac{1}{2}x + 3.
\]

If you can provide the points or any specifics from the graph, I can help you determine the exact equation.

Answer 3

Great! You provided two points on the line: \((-2, 1)\) and \( (2, 3)\). Let's use these points to find the equation of the line in slope-intercept form \(y = mx + b\).

### Step 1: Calculate the slope \(m\)

The slope \(m\) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((-2, 1)\) as \((x_1, y_1)\) and \((2, 3)\) as \((x_2, y_2)\):

\[
m = \frac{3 - 1}{2 - (-2)} = \frac{2}{2 + 2} = \frac{2}{4} = \frac{1}{2}
\]

### Step 2: Find the y-intercept \(b\)

To find the y-intercept, we can use one of the points and the slope. We can substitute \(x\) and \(y\) from either point into the equation \(y = mx + b\) and solve for \(b\). Let's use point \((-2, 1)\):

\[
1 = \frac{1}{2}(-2) + b
\]

Calculating this gives:

\[
1 = -1 + b
\]

Therefore,

\[
b = 1 + 1 = 2
\]

### Step 3: Write the equation in slope-intercept form

Now that we have the slope (\(m = \frac{1}{2}\)) and the y-intercept (\(b = 2\)), we can write the equation of the line:

\[
y = \frac{1}{2}x + 2
\]

### Final Answer

The equation of the line in slope-intercept form is:

\[
y = \frac{1}{2}x + 2
\]

So, filling in the blanks from your original question, it would be:

- **The equation in slope-intercept form is** \(y = \frac{1}{2}x + 2\).