When matching the equation of a line to the graph of a line the things we need to check for are:
- the y-intercept, and
- the slope of the line on the graph.
Let's take these lines on the graph one at a time and examine them.
Detailed
Answers to Initial Practice: Matching a
Graph of a Straight Line with its Equation
Which of the following equations matches the lines A, B, and C in the graph?
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When matching the equation of a line to the graph of a line the things we need to check for are:
Let's take these lines on the graph one at a time and examine them. |
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If you examine the graph, you should notice that the line crosses the y-axis at the point (0, 2). Therefore, the y-intercept is 2.
If you look at line A on the graph, you notice that the y-intercept is 2. In the choices given to choose from, only (f) y = (3/2)x + 2 has a y-intercept of 2. To verify that this is the correct answer, you should calculate the slope of A.
Using the points (2, 5) and (4, 8) from the graph (NOTE: you can use any two points from the graph), the slope is calculated to be:
So the slope of line A is (3/2). A line of slope (3/2) and y-intercept of 2 gives the equation y = (3/2)x + 2.
The equation of line B is (b) y = 6
If you examine the graph, you should notice that the line crosses the y-axis at the point (0, 6). Therefore, the y-intercept is 6.
There is more than one equation here with a y-intercept of 6. Both (b) y = 6 and (d) y = x + 6 have a y-intercept of 6, so you must determine the slope of the line.
Line B is a horizontal line. This means the slope of the line is zero.
A line with y-intercept of 6 and slope of zero has the equation y = (0) x + 6 which is simplified to y = 6.
The equation of line C is (e) y = 4 - (1/3) x.
If you examine the graph, you should notice that the line crosses the y-axis at the point (0, 4). Therefore, the y-intercept is 4. Of our choices, both (a) y = 4 + (1/3) x, and (e) y = 4 - (1/3) x, has a y-intercept of four. Let's take a look at the slope to determine which is the correct answer.
Line C slopes downward to the right. This means that the slope must be negative. y = 4 - (1/3) x also has a negative slope, so is consistent with our answer.
If you had any problems doing this question, please review this unit and then do the additional practice for this unit.
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