Question
Graph this line:
y–5=
–
2(x–7)
Click to select points on the graph.
y–5=
–
2(x–7)
Click to select points on the graph.
Answers
GPT-4o mini
To graph the equation \( y - 5 = -2(x - 7) \), we can first rewrite it in slope-intercept form \( y = mx + b \).
1. Start with the original equation:
\[
y - 5 = -2(x - 7)
\]
2. Distribute \( -2 \) on the right side:
\[
y - 5 = -2x + 14
\]
3. Add 5 to both sides to isolate \( y \):
\[
y = -2x + 14 + 5
\]
\[
y = -2x + 19
\]
Now, we have the equation in slope-intercept form, where the slope \( m = -2 \) and the y-intercept \( b = 19 \).
### Steps to Graph the Line:
1. **Plot the y-intercept**: Start by plotting the point \( (0, 19) \) on the graph.
2. **Use the slope**: From the y-intercept, use the slope to find another point. The slope of -2 means that for every 1 unit you move to the right (positive x-direction), you move 2 units down (negative y-direction).
- Starting at \( (0, 19) \):
- Move 1 unit right to \( (1, 19) \), and then move 2 units down to \( (1, 17) \).
3. **Draw the line**: Connect the points \( (0, 19) \) and \( (1, 17) \) with a straight line, and extend it in both directions.
### Additional Points:
You can also find additional points by substituting values for \( x \):
- If \( x = 2 \):
\[
y = -2(2) + 19 = -4 + 19 = 15 \quad \Rightarrow (2, 15)
\]
- If \( x = 3 \):
\[
y = -2(3) + 19 = -6 + 19 = 13 \quad \Rightarrow (3, 13)
\]
- If \( x = -1 \):
\[
y = -2(-1) + 19 = 2 + 19 = 21 \quad \Rightarrow (-1, 21)
\]
### Graph Points:
Plot these additional points as well \( (2, 15), (3, 13), (-1, 21) \) and ensure your line passes through all these points.
Now you should have a prepared graphical representation of the line \( y = -2x + 19 \). If you can plot these points onto a graphing tool or paper, you can visualize the line.
1. Start with the original equation:
\[
y - 5 = -2(x - 7)
\]
2. Distribute \( -2 \) on the right side:
\[
y - 5 = -2x + 14
\]
3. Add 5 to both sides to isolate \( y \):
\[
y = -2x + 14 + 5
\]
\[
y = -2x + 19
\]
Now, we have the equation in slope-intercept form, where the slope \( m = -2 \) and the y-intercept \( b = 19 \).
### Steps to Graph the Line:
1. **Plot the y-intercept**: Start by plotting the point \( (0, 19) \) on the graph.
2. **Use the slope**: From the y-intercept, use the slope to find another point. The slope of -2 means that for every 1 unit you move to the right (positive x-direction), you move 2 units down (negative y-direction).
- Starting at \( (0, 19) \):
- Move 1 unit right to \( (1, 19) \), and then move 2 units down to \( (1, 17) \).
3. **Draw the line**: Connect the points \( (0, 19) \) and \( (1, 17) \) with a straight line, and extend it in both directions.
### Additional Points:
You can also find additional points by substituting values for \( x \):
- If \( x = 2 \):
\[
y = -2(2) + 19 = -4 + 19 = 15 \quad \Rightarrow (2, 15)
\]
- If \( x = 3 \):
\[
y = -2(3) + 19 = -6 + 19 = 13 \quad \Rightarrow (3, 13)
\]
- If \( x = -1 \):
\[
y = -2(-1) + 19 = 2 + 19 = 21 \quad \Rightarrow (-1, 21)
\]
### Graph Points:
Plot these additional points as well \( (2, 15), (3, 13), (-1, 21) \) and ensure your line passes through all these points.
Now you should have a prepared graphical representation of the line \( y = -2x + 19 \). If you can plot these points onto a graphing tool or paper, you can visualize the line.