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Find an equation of a line whose $y$ -intercept is 4 and such that the area of the triangle formed by the line and the two axes is 20 square units.( Two possible answers.)

$5 y+2 x=20,5 y-2 x=20$

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Judy T.

July 27, 2021

Find the length of the portion of the line 15x – 14y = 210 that is cut off by the axes.

Oregon State University

McMaster University

Harvey Mudd College

Baylor University

Lectures

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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 of two lines. They satisfy some given conditions. What do we know? Well, first, I know that the Y intercept is for okay. Which means it's going to be going through the 0.4 I know that piece. And I also know that this line is going to cut a triangle between the axes and my line. I'm gonna have a triangle in the area of that triangle is gonna be 20 square units, so the area of the triangle that it creates equals 20 square units. So let's kind of try to visualize that, see what that looks like. So let's say I have um Here's my axes X and Y. I know that the Y intercept is for okay, and I'm gonna be cutting a triangle between my axes. So I have two options. My line could go this way, in which case I have this blue triangle here Or if I use Green to show the other one, I could have my line go that direction and I'll have a triangle here now says I want the areas to be the same thes air going to be symmetric. Okay? Because if I look the base, I'll just put this in red. The base would be along the X axis. They share the same height. Their height is four. So if I'm looking at the area of a triangle area of a triangle is one half the base times the height. I know the areas 20. The base is what I don't know. And I'm going to just write this out is based. I don't want to be any confusion between the B that we've been using for the Y intercept and the B for base. This be here is the base of these triangles, and my height is for right. Well, if I want to solve this for the base, the base has to equal 10. Okay. So I could go out 10 on either side. So these X intercepts, I've got two options. One could be at the 10.10 0, and one could be at the point Negative 10 0. So let's take a look. And I'm just gonna We're gonna look at these one at a time. So, um, let's do our green one first. Okay? My green line. The green area that point that X intercept would be the 10.0.10 0. Let's find the slope of that line. Okay, well, let me just actually let me just put our other point on here. This point here is my white intercept. That 0.0.0.4 and I'm going to use that as my first point is, I'm finding the slope. Remember, Slope we find by taking the difference of my wise over the difference of my exes that change in y over the change in X. So for my green line will say that why one is four that be my y intercept minus wife's up to. That's gonna be zero. And then for my exes, that zero minus 10. So I have four over negative 10, and I can just simplify that to negative 2/5 it. So that's my slope. I have the y intercept. I have a slope. So I could just write this in slope intercept form. Why equals M X? There's my slope plus B plus four by. Why Intercept? So that's my first line. Now let's go to our blue line. And again, we're gonna do the same thing. The difference of my wise, the difference in my exes. So why one again? We'll start with that Y intercept points. We have four minus zero over zero minus negative. 10. That gives me a positive four tents or 2/5. And it makes sense that these slopes gonna look very much alike because these air symmetrical shapes Okay, so again, I have slope. I have the intercept. So this time my slope is positive to 50 x. Same. Why? Intercept of positive for? So those are my two possible equations, one that gives me that green triangle one that gives me that blue triangle.

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