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Answer:
- slope = -2/3
- y-intercept: 3, or (0, 3)
- equation: y = -2/3x + 3
- x-intercept: 4.5, or (4.5, 0)
Step-by-step explanation:
When you have a bunch of similar problems, it pays to spend a little time figuring out how to do them quickly.
Here, the questions ask for the x- and y-intercepts, the slope, and the equation.
The x- and y-intercepts can be read from the graph, where the line crosses the x- and y-axes.
The equation likely will need to be in slope-intercept form, so will make use of the y-intercept value.
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Here, the line crosses the y-axis at a grid line, so the y-intercept is an integer. We assume that will be the case for all of your problems. (If not, see the additional comments, below.)
Find the first point to the right of the y-axis where the graph crosses a grid intersection. Here, it is the point (3, 1). Note where it is in relation to the y-intercept. Here, it is 2 units down, and 3 units right, so the slope is ...
m = rise/run = -2/3
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The y-intercept is b = 3, so the equation is ...
y = mx + b
y = -2/3x + 3
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The x-intercept can be found by solving the above equation when y=0, but is more easily read from the graph. The x-intercept is 4.5.
In summary:
- slope = -2/3
- y-intercept: 3, or (0, 3)
- equation: y = -2/3x + 3
- x-intercept: 4.5, or (4.5, 0)
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<em>Additional comments</em>
If the y-axis crossing is not at a grid-line intersection, then find a grid intersection that <em>is</em> on the line. Then find the nearest grid intersection to that one that is also on the line. The slope will be the difference in y-values divided by the <em>corresponding</em> difference in x-values. If the line goes down to the right, the slope will be negative (as here). The reason for using the <em>nearest</em> crossing points is that it gives you a reduced fraction for the slope.
It is important to subtract the y-values in the same order as the x-values. Usually, you will want the x-difference to be positive, so you"re subtracting the left point values from the right point values.
