Question
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Tutor-Verified Answer
Answer
The slope of the line
is 5.
Solution
The given equation of the line is:
This equation is in the slope-intercept form, which is:
Where:
-
is the slope of the line. -
is the y-intercept (the point where the line crosses the y-axis).
Comparing the given equation to the slope-intercept form:
Therefore, the slope of the line is 5.
Understanding the Slope:
- The slope indicates the steepness of the line.
- A slope of 5 means that for every unit increase in
, increases by 5 units. - Graphically, the line rises sharply as you move from left to right.
Example:
If
:
So, the point (0, 12) is on the line.
If
:
So, the point (1, 17) is on the line.
The change in
divided by the change in
between these two points is:
This confirms that the slope is indeed 5.
Answered by UpStudy AI and reviewed by a Professional Tutor
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The Deep Dive
In the equation
, the slope is the coefficient of
, which is 5. This means for every 1 unit you move to the right along the x-axis, the line moves up 5 units on the y-axis. So, grab your graphing tools and get ready to rise steeply!
Visualize this: if you were a climber working your way up a mountain, your ascent would be at a steep angle, making it a bit more challenging but definitely rewarding! The steepness of 5 indicates a sharper incline, which can be quite exciting if you’re picturing road trips along mountain roads.