Which of the following equations matches the lines A and B in the graph.

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.

The equation of line A is (d) y = 4 + 2x

• the y-intercept,

  If you examine the graph, you should notice that line A crosses the y-axis at the point (0, 4). Therefore, the y-intercept is 4.

  Of the choices given, (a) y = 4 - 2 x, and (d) y = 4 + 2 x, both have a y-intercept of 4. To determine which is the correct answer, we must look at the slope of the line for each equation.

• the slope of the line on the graph.

  As you should notice, line A slopes upward. This means the slope is postive. Given this, the answer must be (d) y = 4 + 2 x. But, just to make sure, let's calculate the slope of the line A from two points.

  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 (f) y = 14 - (2/3)x

• the y-intercept,

  If you examine the graph, you should notice that the line crosses the y-axis at the point (0, 14). Therefore, the y-intercept is 14.

  Of the choices given, (b) y = (2/3)x + 14, (e) y = 14 - (3/2)x, and (f) y = y = 14 - (2/3)x, all have a y-intercept of 14. To determine which is the correct answer, we must look at the slope of the line for each equation.

• the slope of the line on the graph.

  Line B slopes downward. This means the slope of the line is negative. Two of our choices have both a negative slope, (e) y = 14 - (3/2) x, and (f) y = 14 - (2/3) x. To determine the correct solution we will have to calculate the slope of line B using two points.

  Using the points (3, 12) and (6, 10) from the graph (NOTE: you can use any two points from the graph), the slope is calculated to be:

  

  So the slope of line B is (-2/3). The equation with a slope of (-2/3) and y-intercept of 14 is (f) y = 14 - (2/3)x.

If you feel comfortable with this material, move in to the summary.

If you still do not understand how to determine if the slope is positive, negative, zero or infinite, you may need more review than is offered by this tutorial. If this is the case, please speak with your professor for suggestions on how to get help.

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