Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Using the previous exercise, determine the equation of the line with intercepts (a) (3,0),(0,6) (b) (2,0),(0,-4) (c) $(1 / 2,0),(0,2 / 3)$

(a) $2 x+y=6$(b) $2 x-y=4$(c) $4 x+3 y=2$

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Oregon State University

McMaster 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).

03:18

01:42

Use the intercept form to …

01:39

02:09

01:24

02:07

Intercept Form of the Equa…

for this problem. We're going to use the equation that we came up with in the previous exercise, number 86. In that exercise, we saw that X over a plus. Why? Over B equals one or a was the X intercept and be was the y intercept? If you do, if you would like to see where we get this equation from, you could go back and look at problem 86 see where this got developed from and then come back. And we're just gonna use it in this particular case. So we're going to try to find three different equations. First, we're gonna have the intercepts 30 and 06 So, as a reminder, A was our X intercept. In this case, they would be three. And B was the y intercept in this case. That's six. So I just plug things in for this particular case. I have X over a I'm sorry. We're actually putting in the numbers here, X over three plus, why over six equals one and I want to write this without fractions. So I'm going to multiply both sides by six. So when I simplify this, I'm going to end up with two X plus. Why? Equal six. Okay, let's try our second case. Our second one. We're gonna have the intercepts. 20 and zero. Negative four. Like I said in the last problem when we were developing this A and B, we have a no assumptions about whether A and B were positive or negative. So just because I have a negative for here, we're gonna use the formula exactly the same way. So when I plug those in, I get X over A. In this case, my ex intercept is too Plus, why over b in this case, it's a negative four equals one. And just to make this look a little nicer instead of doing the plus the negative, I'm just going to change that to be a minus. Okay, Like last time. I don't wanna have fractions in my final answer, so I'm just gonna multiply both sides by four simplifying. That gives me two x minus Y equals four. Okay, last one. This time around, we're going to use, um, fractions. It works exactly the same way. This case, my intercepts are one half zero and 02 3rd. So let's plug those in X over a. So it's X divided by one half. Plus why Overbey. So why over two thirds equals one since we're dividing by fraction of remember, dividing by a fraction is the same is multiplying by its reciprocal. So divided by a half is the same as multiplying by two dividing by two thirds the same is multiplying by three halves equals one And like before, let's get rid of those. Get rid of that fraction gonna multiply everything by two. So that gives me four X plus three y equals two. So those are my three equations using that formula that we developed in the prior exercise.

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:53

Suppose that the manufacturer in Exercise 1 is forced to cut the selling pri…

04:20

Find $y^{\prime}$ if $y=\frac{\left(x^{2}-1\right)^{3}}{\left(x^{2}+1\right)…

01:05

Compute the indicated limit.$$\lim _{x \rightarrow \infty} \frac{5 x^{2}…

05:54

Determine (a) $\lim _{x \rightarrow 3^{+}} \frac{|x-3|}{x-3}\left(\text { b)…

01:17

Use the appropriate rules to determine the derivative.$$y=3 x^{2}-2 x+1,…

03:26

Consider $f(x)=4 x^{2 / 3},$ suppose you do not have a calculator and want t…

01:07

In Example $7,$ find the relationship between $n$ and $x$ in the two methods…

04:46

Find $d y / d x$ at the indicated point in two different ways: (a) Solve for…

01:38

$f(x)=\left(x^{2}+3 x+1\right)^{17},$ find $f^{\prime}(x)$.

02:06

Compute the indicated limit.$$\lim _{x \rightarrow \infty} \frac{(4 x-3)…