Question
Give the slope and the \( y \)-intercept of the line with the given equation. Then, graph the linear equation. \( y=2 x+8 \) fill in any answer boxes within your choice. A. The \( y \)-intercept is (Type an integer or a simplified fraction.) B. There is no y-intercept.
Ask by Goodwin Mullins. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
A. The y-intercept is 8.
B. (Not applicable.)
Solution
The equation is given in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
• Slope (m): 2
• Y-intercept (b): 8, which is the point (0, 8)
Answer Box:
A. The y‑intercept is 8.
B. (Not applicable.)
Graphing the equation:
1. Start at the y‑intercept (0, 8) on the y‑axis.
2. Since the slope is 2 (which means "rise over run" is 2/1), move up 2 units and 1 unit to the right to reach the next point (1, 10).
3. Draw a straight line through these points to complete the graph.
The graph would look like this:
|
12| /
11| /
y 10| ●
9| /
8|●-----
7| /
6| /
5| /
4| /
3|/
2|
1|
0|----------------
0 1 2 3 4 x
The line continues through these points in both directions.
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Simplify this solution Mind Expander
The slope of the line \( y = 2x + 8 \) is 2, meaning for every unit increase in \( x \), \( y \) rises by 2 units. The \( y \)-intercept occurs when \( x = 0 \), which gives us \( y = 8 \). So the \( y \)-intercept is 8! A. The \( y \)-intercept is 8. To graph this line, start at the point \( (0, 8) \) on the y-axis. From there, use the slope of 2 to plot more points—move up 2 units and right 1 unit for each step. Draw a straight line through the points you plotted to finish your graph! B. There is no y-intercept.
