Question

Use the image to answer the question.

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 4 right parenthesis and left parenthesis 1 comma 8 right parenthesis.

Derive the equation of the line in slope-intercept form.

(1 point)
Remaining Attempts : 3
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Answer 1

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

1. **Find the slope (\( m \))**:
The slope of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:

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

Using the points \((0, 4)\) and \((1, 8)\):

\[
m = \frac{8 - 4}{1 - 0} = \frac{4}{1} = 4
\]

2. **Use the slope to find the y-intercept (\( b \))**:
We can use one of the points to solve for \( b \). We'll use the point \((0, 4)\):

\[
y = mx + b
\]
\[
4 = 4(0) + b
\]
\[
4 = b
\]

3. **Write the equation**:
Now that we have both \( m \) and \( b \), we can write the equation in slope-intercept form:

\[
y = 4x + 4
\]

Thus, the equation of the line is:

\[
\boxed{y = 4x + 4}
\]