Question
How do I graph the linear equation 8x+5y=35?
Answers
GPT-4o mini
To graph the linear equation \(8x + 5y = 35\), you'll want to follow these steps:
1. **Rewrite the equation in slope-intercept form (y = mx + b)**:
Start by solving the equation for \(y\).
\[
8x + 5y = 35
\]
Subtract \(8x\) from both sides:
\[
5y = -8x + 35
\]
Now, divide everything by \(5\):
\[
y = -\frac{8}{5}x + 7
\]
This is now in the form \(y = mx + b\) where:
- Slope (\(m\)) is \(-\frac{8}{5}\)
- Y-intercept (\(b\)) is \(7\)
2. **Plot the y-intercept**:
The y-intercept is where the line crosses the y-axis. This occurs at the point \((0, 7)\). Plot this point on the graph.
3. **Use the slope to find another point**:
The slope is \(-\frac{8}{5}\), which means that for every \(5\) units you move to the right (positive direction on the x-axis), you move \(8\) units down (negative direction on the y-axis). Starting from the y-intercept \((0, 7)\):
- Move \(5\) units to the right to \(x = 5\).
- From \(y = 7\), move \(8\) units down to \(y = 7 - 8 = -1\).
So, another point is \((5, -1)\).
4. **Plot the second point**:
Plot the point \((5, -1)\) on the graph.
5. **Draw the line**:
Using a straightedge, draw a line through the two points \((0, 7)\) and \((5, -1)\). Extend the line in both directions, adding arrows to indicate that it continues indefinitely.
6. **Check by finding a third point (optional)**:
You can also find a third point by substituting different values for \(x\) and solving for \(y\) or vice versa. For example, if you let \(x = 0\), you get the y-intercept we already found \((0, 7)\). Letting \(y = 0\) would give:
\[
8x + 5(0) = 35 \implies 8x = 35 \implies x = \frac{35}{8} \approx 4.375
\]
So you have the point \((4.375, 0)\) as an alternative.
That's how you graph the linear equation \(8x + 5y = 35\). The resulting line should extend indefinitely and represent all the solutions to the equation.
1. **Rewrite the equation in slope-intercept form (y = mx + b)**:
Start by solving the equation for \(y\).
\[
8x + 5y = 35
\]
Subtract \(8x\) from both sides:
\[
5y = -8x + 35
\]
Now, divide everything by \(5\):
\[
y = -\frac{8}{5}x + 7
\]
This is now in the form \(y = mx + b\) where:
- Slope (\(m\)) is \(-\frac{8}{5}\)
- Y-intercept (\(b\)) is \(7\)
2. **Plot the y-intercept**:
The y-intercept is where the line crosses the y-axis. This occurs at the point \((0, 7)\). Plot this point on the graph.
3. **Use the slope to find another point**:
The slope is \(-\frac{8}{5}\), which means that for every \(5\) units you move to the right (positive direction on the x-axis), you move \(8\) units down (negative direction on the y-axis). Starting from the y-intercept \((0, 7)\):
- Move \(5\) units to the right to \(x = 5\).
- From \(y = 7\), move \(8\) units down to \(y = 7 - 8 = -1\).
So, another point is \((5, -1)\).
4. **Plot the second point**:
Plot the point \((5, -1)\) on the graph.
5. **Draw the line**:
Using a straightedge, draw a line through the two points \((0, 7)\) and \((5, -1)\). Extend the line in both directions, adding arrows to indicate that it continues indefinitely.
6. **Check by finding a third point (optional)**:
You can also find a third point by substituting different values for \(x\) and solving for \(y\) or vice versa. For example, if you let \(x = 0\), you get the y-intercept we already found \((0, 7)\). Letting \(y = 0\) would give:
\[
8x + 5(0) = 35 \implies 8x = 35 \implies x = \frac{35}{8} \approx 4.375
\]
So you have the point \((4.375, 0)\) as an alternative.
That's how you graph the linear equation \(8x + 5y = 35\). The resulting line should extend indefinitely and represent all the solutions to the equation.