Answer:
- see below for a graph
- x-intercept: -8
- y-intercept: 2 2/3
- slope: 1/3
Explanation:
First of all, recognize that the equation is in the form ...
y -k = m(x -h) . . . . . . . . . point-slope equation of a line
with (h, k) = (-2, 2) and m = 1/3.
(a) In the point-slope form of the equation for a line, the slope of the line and a point it goes through can be read from the equation. Here, we see that m=1/3 means the slope of the line is 1/3. The (h, k) values mean the line goes through the point (-2, 2).
When drawing the graph, it is convenient to plot the point you know (-2, 2), and then find another point on the graph based on the slope.
The slope of 1/3 means the line will rise 1 unit for each 3 units to the right. Working to the right from the point you know, you can tell that (1, 3) will be another point on the graph (1 up and 3 right). Working to the left, you can tell that points (-5, 1) and (-8, 0) will be on the graph. (1 down and 3 left from the previous point)
The graph can be drawn by drawing a straight line through those points.
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(b) The graph (and the above list of points) tells you that the x-intercept is -8. That is, the graph goes through the point (-8, 0).
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(c) The y-intercept is not on a grid line, so finding its value from the graph could be difficult. It is easier to solve the equation for x=0 to find the y-intercept:
y -2 = (1/3)(0 +2) . . . . . . put 0 where x is
y = 2 + 2/3 . . . . . . . . . . . add 2 and simplify a bit
y = 2 2/3 . . . . . . . . . . . . show the y-intercept as a mixed number
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(d) We read the slope from the given equation in part A. The slope is 1/3.