Question

Graph the function.
y=4–
7
2
x–1

1-8 x and y axis

Answer 1

To graph the function \( y = 4 - \frac{7}{2} x - 1 \), let's first simplify it:

Starting with:
\[
y = 4 - \frac{7}{2} x - 1
\]
Combine like terms:
\[
y = 3 - \frac{7}{2} x
\]

Next, we can rewrite it as:
\[
y = -\frac{7}{2}x + 3
\]
This is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Key Features of the Function:
1. **Y-Intercept**: When \( x = 0 \):
\[
y = 3
\]
So the y-intercept is \( (0, 3) \).

2. **Slope**: The slope \( m = -\frac{7}{2} \) tells us that for every 2 units we move to the right (positive x-direction), we move 7 units down (negative y-direction).

### Finding Another Point:
Let’s find another point by choosing \( x = 2 \):
\[
y = -\frac{7}{2}(2) + 3 = -7 + 3 = -4
\]
So the point \( (2, -4) \) is also on the line.

### Plotting the Points:
Now we can plot the points:
- Y-intercept: \( (0, 3) \)
- Another point: \( (2, -4) \)

### Graphing the Line:
1. Start at the point \( (0, 3) \) on the y-axis.
2. From there, use the slope to find the next point: from \( (0, 3) \) move 2 units to the right to \( x=2 \), and down 7 units to get \( (2, -4) \).
3. Draw a straight line through these points extending in both directions.

### X-Intercept:
To find the x-intercept where \( y = 0 \):
\[
0 = -\frac{7}{2}x + 3
\]
\[
\frac{7}{2}x = 3
\]
\[
x = \frac{3 \cdot 2}{7} = \frac{6}{7}
\]
So the x-intercept is \( \left( \frac{6}{7}, 0 \right) \).

Now your graph should have:
- The y-intercept \( (0, 3) \),
- The x-intercept \( \left( \frac{6}{7}, 0 \right) \),
- Point \( (2, -4) \).

You can draw the graph on a coordinate plane, making sure to label the axes and the intercept points!