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Determine an equation for the line parallel to $y=3 x-7$ and passing through the point $(1,-5)$.

$y=3 x-8$

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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for this problem. We're trying to find the equation for a particular line. We know the line we're looking for is parallel to a given line. We wanted to be parallel to the line. Why equals three X minus seven? We also know that we want the line to pass through the 0.1 negative five. Well, anytime were given a point, especially if it's just one point. If it's not the intercept. Ah, good thing to think about is point Slope for as a reminder point slope form looks like this. Why? Minus why one equals m times X minus X one. So the point would be X one y one, which we have. The only other piece of information we need to make this work is the slope. So let's go back to the other piece of information We know we know that we want to be parallel to a given line. Well, what does it mean? If two lines are parallel? If I have a line? No, just I'm just drawing a line here. Just some random line. A parallel lied to. This could be that line or this one or this one we know to be parallel. They have to rise and fall at exactly the same rate. Well, that rate at which you rise and fall is this slope. So if they rise and fall at the same rate, they have the same slope. So the line I'm looking for has a slope equal to the slope of our given line. Now this line is given to us in slope intercept form. So to find our slope, we just look at the coefficient off the X term. So our slope in this case is three. So I have a point. I have a slope. I can use the point slope form. Why? Minus the y coordinate. Negative five. Subtracting a negative is like a adding. So I have white plus five equals my slope, which is three times x minus X up one. Will the X coordinate? My point is one. And now it's just a matter of making this look a little nicer. We'll get rid of our parentheses to be three x minus three and then we'll subtract five from both sides. So our final form of our line why equals three X minus eight

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