Question
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Answer
The equation
has a slope of
, a
-intercept at
, and an
-intercept at
.
Solution
-
Identify the form of the equationThe equationis in slope-intercept form, which iswhere
is the slope and is the -intercept. -
Determine the slope and
-intercept -
The slope is
-
The
-intercept is This means the line crosses the-axis at the point .
-
-
Find the
-intercept To find the-intercept, set and solve for : Multiply each term by 8 to eliminate the fraction:Solve for: So, the-intercept is . -
Summary
- Slope:
-
-intercept: -
-intercept:
- Slope:
This breakdown explains all the important features of the linear equation.
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Mind Expander
This equation describes a straight line in slope-intercept form, where the slope is
and the y-intercept is
. This means for every 8 units you move to the right along the x-axis, you move up 3 units along the y-axis. If you were to graph it, you’d start at the point
on the y-axis and use the slope to find other points on the line.
In real-world scenarios, this linear equation might represent a relationship between two variables—like distance and fuel consumption or cost and quantity. Imagine you’re budgeting your expenses: if your company charges a flat fee of 3 (the starting point), and then adds a smaller incremental charge that scales with usage (represented by
), you could predict costs based on usage!