Question

Graph the equation 9−x=3/2y
using slope-intercept form.(1 point)
Responses

A) A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma 3 right parenthesis, and left parenthesis 4 comma 2 right parenthesis.

B) A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 3 right parenthesis, and left parenthesis 7 comma negative 1 right parenthesis.

C) An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. A downward slanting line is graphed on the coordinate plane. The downward slanting line passes through closed points plotted at left parenthesis 0 comma 6 right parenthesis and left parenthesis 3 comma 4 right parenthesis.

D) A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 2 comma 1 right parenthesis.

Answer 1

To graph the equation \(9 - x = \frac{3}{2}y\), we first need to convert this equation to the slope-intercept form \(y = mx + b\).

Starting from the original equation:

\[
9 - x = \frac{3}{2}y
\]

We can rearrange this to solve for \(y\):

First, isolate \(\frac{3}{2}y\):

\[
\frac{3}{2}y = 9 - x
\]

Next, multiply both sides by \(\frac{2}{3}\) to solve for \(y\):

\[
y = \frac{2}{3}(9 - x)
\]

Distributing the \(\frac{2}{3}\):

\[
y = \frac{2}{3} \cdot 9 - \frac{2}{3}x
\]

\[
y = 6 - \frac{2}{3}x
\]

Now, we have the equation in slope-intercept form:

\[
y = -\frac{2}{3}x + 6
\]

From this form, we can identify that the slope \(m = -\frac{2}{3}\) and the y-intercept \(b = 6\).

To graph this line, we can start by plotting the y-intercept (0, 6) and using the slope to find another point. From (0, 6), going down 2 units and to the right 3 units (since our slope is negative), we find the point (3, 4).

Now let’s look for the responses that fit the description of our line.

- **Checking the options**:
- **A)** Plotted points (0, 3) and (4, 2) do not match.
- **B)** Plotted points (0, -3) and (7, -1) do not match.
- **C)** Points (0, 6) and (3, 4) do match.
- **D)** Plotted points (0, 0) and (2, 1) do not match.

Thus, the correct response is C.