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Find the slope, $x$ -intercept and $y$ -intercept of the given line.$$2 x+4 y-9=0.$$

$-1 / 2,(9 / 2,0),(0,9 / 4)$

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).

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for this problem. We've been given the equation of a line and we want to find three particular things about this line. Specifically, we're going to find it slope in the two intercepts, the X intercept and the Y intercept. Now, in order to solve this type of problem, one of the easiest ways to begin is to put this into slope intercept for, in other words, we're going to solve for why and once we put it in this form, why equals M X plus B? We'll have two of our three pieces of information. The M the coefficient in front of the X term is the slope and be the constant term is our Y intercept Now? Specifically, remember, X and Y thes intercepts are both points. The X intercept has a Y value of zero. The Y intercept has an X value of zero. So in particular this be that we have will actually be the y. Coordinate off the y. Intercept that piece right there is going to be be the X intercept we don't get from this form will find that separately at the end. Okay, so let's go back to our original equation to solve this for wise. We'll start by taking every term. That's not why and putting it to the right hand side. So on the left, we have four y on the right hand side moving that two x becomes a negative two x and the negative nine when remove it becomes a positive nine. Now, I don't just a why on the left hand side So I divide everything by four and I get why equals negative one half X plus 9/4. Okay, so there's our slope intercept form. The coefficient of the X term is our slope. So I slope is negative one half the constant is the y coordinate of the Y intercept. So my Y intercept is 0 9/4 now, my ex intercept, Remember, the X intercept is where the y value is. Zero. So if I'm going to go back up, gonna go copy my original equation again. If why is zero than what I have here is two X plus zero minus nine equals zero. Solve this for X. I'm gonna move that negative nine to the other side. It becomes positive. Nine. I get X equals nine haps. So there's my ex intercept the 0.9 halves zero. So this gives me my slope, my ex intercept and my Y intercept

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