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Find the slope, $x$ -intercept and $y$ -intercept of the given line.$$1.3 x+4.7 y+11.2=0.$$

$-13 / 47,(-112 / 13,0),(0,-112 / 47)$

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Campbell University

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).

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for this problem. We've been given an equation, and we have three things that we want to find related to this equation. First, I want to find the slope, and I want to find the two intercepts, the X intercept and the Y intercept. So in order to best find these, the first thing we're going to do is put our equation into slope intercept form as a reminder that form is y equals MX plus B. So if we solve our equation for why we put it into this format, this is helpful because the M is my slope and B is the Y intercept in particular be is the y coordinate of the Y intercept? We know both the X and the Y intercept our points, but the Y intercept has an X value of 03 X intercept has a Y value of zero. So when we find the values that work for the intercepts, they're gonna go in the blanks. Uh, in those points. Okay, let's go back and look at our original equation. Yeah, this will be easier to deal with without the decimals. So what I'm going to do is I'm going to multiply everything in this equation. Both sides of the equal sign by 10. That gives me 13 X plus 47. Why plus 112 equals zero. Do you have to do this? No. You can leave your decimals in and deal with them later. I just find this is easier to work with. So I like to get rid of the decimals if I can. Okay, let's solve this for why every term that's not did did not contain why I'm going to push to the right hand side. So that means I'll have negative 13 x minus 112 on the right side, and I'll have my 47. Why on the left? Now let's divide both sides by 47. That gives me why equals and I'm gonna break this up into two pieces because it better matches the format that I'm looking for for that slope. Intercept. So it's negative. 13/47 times X minus 112 over 47. So that gives me my slope in my intercept. Why intercept the coordinate? Uh, coefficient in front of the extreme is my slope. So the slope here is negative. 13/47. My, Why intercept is Thedc on stint, including the sign. So that's going to be a negative 1 12/47 for my Y intercept. And now for my ex intercept. That one is not something I could find easily in this format. To find the X intercept. Let's go back to our original equation. Specifically, I'm going to go to the format where I just got rid of my decimals again. I find that easier to work with and I'm going to set. Why equal to zero? That's the definition of X intercept. So if I let Y equals zero, that means what I have left is 13 x 47. Why is now gone? That equals zero plus 1. 12 equals zero and I can solve for X 13 X equals negative 112 or X equals negative 112 over 13 so I can put that number in for the X coordinate of the X intercept point. So here the slope and the two intercepts for our give in line

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