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Find the equation of the line using the information given. Write answers in slope-intercept form.parallel to $12 x+5 y=65,$ through the point (-2,-1)
$y=\frac{-12}{5} x-\frac{29}{5}$
Algebra
Chapter 2
Relations, Functions, and Graphs
Section 3
Linear Graphs and Rates of Change
Graphs and Statistics
Functions
Campbell University
McMaster University
University of Michigan - Ann Arbor
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we have to create the equation of a line which is parallel to the given equation. 12 X plus five equals 65 passes through the point negative to common negative one. First off, we're going to need to find the slope of the original line, so we'll be rearranging this to put it in slope intercept form. First off, we subtract 12 extra both sides giving us five y equals 65 minus 12 X. Now we divide by five to get why, by itself giving us why equals 65/5 is 13 minus 2/5 X. This isn't slope intercept form, which means that the slope is whatever number is multiplied by X. Thus the slope, which is all that we need from this equation, is negative. 12/5. We'll be using that later. Now we need to find the equation for our new line. We're going to be using Point Slope form to do this and then rearranging to get slope intercept form. As the question recommends. Slope Intercept form has the basic format or sorry point Slope form has the basic format. Why minus y one is equal toe m times X minus X one where X one y one is just some point. We'll be using negative to negative one as X one y one. So let's plug stuff into this. We have why minus negative. One is equal to M Times X minus negative, too. What is M well for any pair of parallel lines. The one thing that we know is going to be true based on the definition, is that two parallel lines must have the exact same slope. Therefore, the slope of our new line must be the same as the slope of the old line. Negative 12/5. Let's rearrange a little bit. We have why plus one equals negative. 12 x over five. Now these negatives air going to cancel right here. But then we're going to be multiplying them by another negative, giving us once again a negative number minus 24 12 times two divided by five. Now all we have to do he's moved the one over the other side. Giving us why equals negative 12 x over five minus. Now this one is equal to 5/5, minus 29 or 24 minus 5/5. So there's like that. We now have this in slope intercept form. As you can see, it has the exact same slope as the original equation, but it has a different Y intercept because it has to pass through this point. Negative two comma one. This line will be parallel to the original line, but it now passes through the desired point.
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