Answer:
- 2/3
- -3/4
- -2
- undefined
- 4
- 0
Explanation:
You want to find the slopes of the lines shown in the attached graphs.
Slope
The slope of a line is its "rise" divided by its "run":
m = rise/run
To determine slope from a graph, start at an identified point on the left, and count the grid squares up (+) or down (-) to the same horizontal line as the identified point on the right. This is the "rise". Then count the grid squares horizontally to the identified point. This is the "run". The slope is the ratio of these numbers.
1. rise 4, run 6, slope 4/6 = 2/3
2. rise -3, run 4, slope -3/4
3. rise -6, run 3, slope -6/3 = -2
4. run = 0; division by 0 is "undefined", so the slope is "undefined"
5. rise 4, run 1, slope 4/1 = 4
6. rise 0, run (anything), slope 0/1 = 0
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Additional comment
It is helpful to remember that a horizontal line has a slope of 0, and a vertical line has a slope that is "undefined." Slope is positive if the line goes up to the right. It is negative if the slope goes down to the right.
Because the slope of a vertical line is "undefined," its equation cannot be written in "slope-intercept" form.
Here, points are marked on the lines. When that is not the case, it usually works well to identify points where the line crosses an intersection of grid lines.
You can also use grid crossings to check your answer for the slope. For example, the line on graph 3 crosses grid intersections that are 2 down and 1 over from the marked points (and other grid intersections), confirming a slope of -2.