Question

page 22 of 23
Graphing Equations Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
2 of 52 of 5 Items

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)
y
=
x+

Answer 1

To determine the equation of the line in slope-intercept form (y = mx + b), we first need to find the slope (m) of the line using the two points provided: (0, 4) and (1, 8).

1. **Calculate the slope (m):**
The formula for slope (m) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 4) (let's designate this as (x_1, y_1)) and (1, 8) (let's designate this as (x_2, y_2)):
\[
m = \frac{8 - 4}{1 - 0} = \frac{4}{1} = 4
\]

2. **Use the slope and one point to find the y-intercept (b):**
We can use the slope and either of the points to find the y-intercept. We'll use the point (0, 4):
\[
y = mx + b
\]
Substituting in the values from the point (0, 4):
\[
4 = 4(0) + b
\]
\[
b = 4
\]

3. **Write the equation in slope-intercept form:**
Now that we have both the slope and the y-intercept, we can write the equation:
\[
y = 4x + 4
\]

So, the final answer is:
\[
y = 4x + 4
\]