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

In general, how are the lines $y=m x+b$ and $y-k=m(x-h)+b \mathrm{re}-$ lated? ( $m, b, h,$ and $k$ are constants.)

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Missouri State University

McMaster University

Baylor 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

01:07

Suppose that $A$ and $B$ a…

05:21

Slope of a line Consider t…

00:39

Are the lines parallel?

01:42

A line passes through $\le…

06:36

Given the two parallel lin…

for this problem, we're going to compare to generic lines. Our first line. We're just going to write in typical slope intercept for why equals m X plus B for our second line, we're gonna make a couple of small changes. Were instead of why we're gonna have y minus k instead of X, we're gonna have X minus. H m and B are going to remain unchanged, so we just kind of want to compare these. How are these lines related to each other? Well, as you can see, they have the same slope. I'm not doing anything to that M. And if I If I use the distributive property and multiplied out that second one, I'm still gonna end up with M X. So the first thing we can see for sure is that these air parallel lines they have identical slopes. Now what changes, though, are my why and my ex variables, I'm doing something to those. And after we talk about this, if you want to see it in action, you could go back and look at the prior three exercises 82 83 84. They kind of go into this idea with some specific examples so you can see how the general cases would map to a couple of specific lines. So when we change a variable, for example X If I add or subtract something directly to that x variable, what that gives me is a horizontal shift. It shifts my entire line or function. Whatever I have, it shifts it left and right, and it shifts it H units. Right? And I'm so so, um, subtracting this so x minus h that that means I'm shifting h units. If it's plus, I'm gonna be shifting it to the left. If it's a subtraction like X minus three or X minus four, that's a shift to the right. So you're gonna be subtracting that shift so that H is gonna tell you how far we shift left or right? Likewise, since exes horizontal, why is going to be vertical? So if we're adding or subtracting something to our Y variable, that's going to give us a vertical shift, and we're gonna be shifting by K units. So why minus one means I'm shifting up One unit, Why minus three is an upper shift of three. That K tells me how far I go up. If it's a plus, that means I'm shifting by a negative number. That means I'm gonna be going down. So X plus two would be a shift downward of two. X y plus five is a downward shift of five. So in general, if you see something in this format, the H tells you how far you shift left and right. The K tells you how far you shift up and down.

View More Answers From This Book

Find Another Textbook

02:21

Find the equations of the lines and plot the lines from Exercise $57$.

12:26

Given the triangle with vertices $A(1,1), B(3,7),$ and $C(9,3)$. (a) Determi…

02:22

Compute the indicated limit.$$\text { (a) } \lim _{x \rightarrow \infty}…

01:27

Use your knowledge of the derivative to compute the limit given.$$\lim _…

09:14

Show that the area of the triangle in the first quadrant formed by the tange…

04:01

Determine the equation of the perpendicular bisector of the line joining the…

02:17

Determine the coordinates of the midpoint of the line segment joining the po…

01:18

Given the graph of the function $y=f(x)$ in Figure $30,$ draw the graph with…

04:30

Find the point on the line $y=2 x+3$ that is equidistant from the points $(-…

01:04

The maximum possible demand for a certain commodity is 20,000 tons. The high…