Question
Solve for y and graph the equation with a standard window on a graphing utility.
4 x minus 3 y equals 4
4 x minus 3 y equals 4
Answers
GPT-4o mini
To solve for \( y \) in the equation \( 4x - 3y = 4 \), follow these steps:
1. Start with the equation:
\[
4x - 3y = 4
\]
2. Isolate the term with \( y \):
\[
-3y = 4 - 4x
\]
3. Divide each term by \(-3\) to solve for \( y \):
\[
y = \frac{4 - 4x}{-3}
\]
\[
y = -\frac{4}{3} + \frac{4}{3}x
\]
This can be rearranged to the slope-intercept form \( y = mx + b \):
\[
y = \frac{4}{3}x - \frac{4}{3}
\]
### Graphing the equation
1. To graph this line, we can identify the slope and \( y \)-intercept. The slope \( m \) is \( \frac{4}{3} \) and the \( y \)-intercept \( b \) is \(-\frac{4}{3}\).
2. Plot the \( y \)-intercept at \( (0, -\frac{4}{3}) \), which is approximately \((0, -1.33)\).
3. From the \( y \)-intercept, use the slope to find another point. Since the slope is \( \frac{4}{3} \), for every 3 units you go to the right (positive \( x \)), you go up 4 units (positive \( y \)).
4. Starting from \( (0, -\frac{4}{3}) \), if you move 3 units to the right to \( x = 3 \), you move up 4 units to approximately \( y = 1.67 \), giving a point at \( (3, 1.67) \).
5. You can also find other points using the x-intercept. Set \( y = 0 \):
\[
0 = \frac{4}{3}x - \frac{4}{3}
\]
\[
\frac{4}{3}x = \frac{4}{3} \quad \Rightarrow \quad x = 1
\]
So the x-intercept is at \( (1, 0) \).
### Final Steps
With the points \( (0, -\frac{4}{3}) \), \( (3, 1.67) \), and \( (1, 0) \), you can graph the line. Be sure to draw a straight line through these points.
If you're using a graphing utility, you can input the equation in the form \( y = \frac{4}{3}x - \frac{4}{3} \) and set the window to a standard view, typically \( x: [-10, 10] \) and \( y: [-10, 10] \). This will give you a clear view of the line.
1. Start with the equation:
\[
4x - 3y = 4
\]
2. Isolate the term with \( y \):
\[
-3y = 4 - 4x
\]
3. Divide each term by \(-3\) to solve for \( y \):
\[
y = \frac{4 - 4x}{-3}
\]
\[
y = -\frac{4}{3} + \frac{4}{3}x
\]
This can be rearranged to the slope-intercept form \( y = mx + b \):
\[
y = \frac{4}{3}x - \frac{4}{3}
\]
### Graphing the equation
1. To graph this line, we can identify the slope and \( y \)-intercept. The slope \( m \) is \( \frac{4}{3} \) and the \( y \)-intercept \( b \) is \(-\frac{4}{3}\).
2. Plot the \( y \)-intercept at \( (0, -\frac{4}{3}) \), which is approximately \((0, -1.33)\).
3. From the \( y \)-intercept, use the slope to find another point. Since the slope is \( \frac{4}{3} \), for every 3 units you go to the right (positive \( x \)), you go up 4 units (positive \( y \)).
4. Starting from \( (0, -\frac{4}{3}) \), if you move 3 units to the right to \( x = 3 \), you move up 4 units to approximately \( y = 1.67 \), giving a point at \( (3, 1.67) \).
5. You can also find other points using the x-intercept. Set \( y = 0 \):
\[
0 = \frac{4}{3}x - \frac{4}{3}
\]
\[
\frac{4}{3}x = \frac{4}{3} \quad \Rightarrow \quad x = 1
\]
So the x-intercept is at \( (1, 0) \).
### Final Steps
With the points \( (0, -\frac{4}{3}) \), \( (3, 1.67) \), and \( (1, 0) \), you can graph the line. Be sure to draw a straight line through these points.
If you're using a graphing utility, you can input the equation in the form \( y = \frac{4}{3}x - \frac{4}{3} \) and set the window to a standard view, typically \( x: [-10, 10] \) and \( y: [-10, 10] \). This will give you a clear view of the line.