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Find the equations of the lines and plot the lines from Exercise $53$.

$14 x+2 y=3$

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Missouri State University

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McMaster University

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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Find the equations of the …

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Find the equation of the l…

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Finding an Equation of a L…

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Plot the pair of points an…

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for this problem, we're going to be referencing exercise number 53 from earlier in this lesson. Now, in exercise 53 we were given two points, the 20.1 half negative too. And the 0.1 quarter negative one quarter. And in that exercise, we found the slope of the line that connects those points. We found the slope to be negative seven. Okay, now that's the background for this problem. We want to find the equation of the line that this describes and then graph that line so often we use the slope intercept form. Why equals MX plus B? Unfortunately, we don't have be We don't have our intercept here. What we do have, though, is a point that we have two points and the slope so we can use the point slope for why minus why one equals m times X minus X one. So x one y one is a point that we have. It actually doesn't matter which point we use. Any point on this line will satisfy this equation. So we will just randomly pick one of these points when it comes time to do the math here, So x one and why one is our point. And there's our slope M. So let's plug things in, uh, again, it doesn't matter which point. I'm just going to take the first point because it's first. Why minus why one? So that's gonna be subtracting a negative, too. Or plus two equals my slope. Negative seven x minus X one, which is one half. Let's get rid of our parentheses. That's a negative seven X plus seven halfs and then I'm gonna subtract two from both sides. So when I subtract two common denominator that's actually subtracting oops did me to write it there before four halfs? So final result for this equation is why equals negative seven X plus three halves. Okay, so there's my equation. Now let's come over here and graph what we have. First, we need a starting point. So let's start with our Y intercept three halves. So that's going to be right about there, right between the 1st and 2nd grid lines. There. Now, our slope are slope is negative. Seven negative slope means that my line we trending downwards. I go from left to right across my grid and to see that rise over run. I'm gonna put that negative 7/1. So when I wanna look at rise overrun, I'm gonna rise. Negative seven. Otherwise, it was dropping seven. And then I run one unit sideways, so I'm gonna go down. 71234567 and over one. Um, and there's not a whole lot more room down there, so I'm gonna go up the other direction to get my other point. 1234567 and over one. You can draw a line with two points for me. Three points. Helps make sure that I'm nice and straight as I connect my lines. Okay, So there is the graph of this equation. Why equals negative seven x plus three halves?

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