Pearson Algebra 1 Common Core, 2011
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Pearson Algebra 1 Common Core, 2011 View details
Mid-Chapter Quiz
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Exercise 23 Page 321

Recall and implement two different forms of the line equation.

See solution.

Practice makes perfect

Suppose that we have the graph shown below.

Using this example graph, we will illustrate two methods to find the equation of a line given its graph.

Finding the Equation Using the Point-Slope Form

One way is to use the point-slope form.

y-y_1 = m (x-x_1) Here m is the slope of the line and (x_1,y_1) is a known point on the line. The first thing to do is to identify a point. Then, we can move from it while counting the rise and the run to find the slope.

In our example, we identify the point (0,1). We can see that when the run is 2 we have a rise of 3 units. Let's calculate the slope.
m = rise/run
m = 3/2
m = 1.5
Now we substitute the found values into the point-slope form to get our line equation.
y-y_1 = m (x-x_1)
y-1 = 1.5 (x-0)
y-1 = 1.5x
y= 1.5 x +1
The corresponding line equation for the example graph is y= 1.5 x +1.

Finding the Equation Using the Slope-Intercept Formula

We can also find the line equation using the slope-intercept form. y = mx + b Here m is the slope of the line and b is the y-intercept. Once again, let's start by identifying these features in the graph.

We now proceed to calculate the slope, just as we did above. We will not show that again, and we will just use its value — m=1.5. We can see from the graph that in this case, b=1. If we substitute these values into the slope-intercept form, we will find our line equation. y = 1.5x + 1