Question

Use the image to answer the question. Use the graph to derive the equation of the line in slope-intercept form. (1 point) y= x- Skip to navigation An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 1 comma 3 right parenthesis."/>

Answer 1

To derive the equation of the line in slope-intercept form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).

1. **Calculate the Slope (m):**
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, we will use the points \( (0, -2) \) and \( (1, 3) \).
\[
m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5
\]

2. **Use the Slope to Find the Y-Intercept (b):**
We know the slope \( m = 5 \). We can use one of the points to find the y-intercept \( b \). Let’s use the point \( (0, -2) \):
\[
y = mx + b
\]
Using the point \( (0, -2) \):
\[
-2 = 5(0) + b \Rightarrow -2 = b
\]

3. **Write the Equation:**
Now that we have the slope and the y-intercept, we can write the equation of the line:
\[
y = 5x - 2
\]

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