Question

a graph with (0 , -2) and (1 , 3)

Use the graph to derive the equation of the line in slope intercept form

Answer 1

you sure

Answer 2

To derive the equation of the line in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, we can follow these steps:

1. **Identify the coordinates of the points**:
- Point 1: \((0, -2)\)
- Point 2: \((1, 3)\)

2. **Calculate the slope (m)**:
The slope \(m\) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the coordinates of the points:
\[
m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5
\]

3. **Find the y-intercept (b)**:
Since we have the y-intercept directly from point \((0, -2)\), we know that \(b = -2\).

4. **Write the equation**:
Now we can substitute \(m\) and \(b\) into the slope-intercept form:
\[
y = 5x - 2
\]

Therefore, the equation of the line in slope-intercept form is:
\[
y = 5x - 2
\]

Answer 3

Let's double-check the calculations for the equation of the line given the points \((0, -2)\) and \((1, 3)\).

1. **Identifying Coordinates**:
- Point 1: \((0, -2)\)
- Point 2: \((1, 3)\)

2. **Calculating the Slope (m)**:
Using the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\):
- Here, \(y_2 = 3\), \(y_1 = -2\), \(x_2 = 1\), and \(x_1 = 0\).
\[
m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1 - 0} = \frac{5}{1} = 5
\]

3. **Finding the Y-Intercept (b)**:
The y-intercept is the value where the line crosses the y-axis. From the given point \((0, -2)\), we see that:
\[
b = -2
\]

4. **Writing the Equation**:
Now, substituting the values of \(m\) and \(b\) into the slope-intercept form \(y = mx + b\):
\[
y = 5x - 2
\]

So, the final equation of the line in slope-intercept form is indeed:
\[
y = 5x - 2
\]

The calculation is confirmed to be correct. If you have any specific concerns or follow-up questions, let me know!