Question
Solve y-5 = -1/4x so I can graph it
Answers
GPT-4o mini
To solve the equation \( y - 5 = -\frac{1}{4}x \) for \( y \), we can isolate \( y \) by adding 5 to both sides:
\[
y = -\frac{1}{4}x + 5
\]
Now the equation is in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
From the equation \( y = -\frac{1}{4}x + 5 \):
- The slope \( m \) is \( -\frac{1}{4} \).
- The y-intercept \( b \) is \( 5 \).
### Graphing the Equation
1. **Plot the y-intercept**: Start by plotting the point (0, 5) on the graph.
2. **Use the slope to find another point**: The slope of \( -\frac{1}{4} \) means that for every 4 units you move to the right (positive x-direction), you move down 1 unit (negative y-direction):
- From (0, 5), move 4 units to the right to (4, 5), and then move down 1 unit to (4, 4).
- Plot the point (4, 4).
3. **Draw the line**: Connect the points (0, 5) and (4, 4) with a straight line, extending it in both directions.
This gives you the graph of the equation \( y - 5 = -\frac{1}{4}x \).
\[
y = -\frac{1}{4}x + 5
\]
Now the equation is in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
From the equation \( y = -\frac{1}{4}x + 5 \):
- The slope \( m \) is \( -\frac{1}{4} \).
- The y-intercept \( b \) is \( 5 \).
### Graphing the Equation
1. **Plot the y-intercept**: Start by plotting the point (0, 5) on the graph.
2. **Use the slope to find another point**: The slope of \( -\frac{1}{4} \) means that for every 4 units you move to the right (positive x-direction), you move down 1 unit (negative y-direction):
- From (0, 5), move 4 units to the right to (4, 5), and then move down 1 unit to (4, 4).
- Plot the point (4, 4).
3. **Draw the line**: Connect the points (0, 5) and (4, 4) with a straight line, extending it in both directions.
This gives you the graph of the equation \( y - 5 = -\frac{1}{4}x \).