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Find the slope, $x$ -intercept and $y$ -intercept of the given line.$$16-4 y=35.$$

$0,(0,-19 / 4)$ , no x-intercept

Algebra

Chapter 1

Functions and their Applications

Section 1

The Line

Functions

Oregon State University

McMaster University

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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00:35

Find the slope and y-inter…

00:45

Determine the slope and $y…

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00:30

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00:25

Find the slope-intercept e…

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Find the $y$ -intercept of…

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03:20

Write the equation of the …

So this problem We have been given an equation and we need to find three different things related to this equation. Specifically, we're looking for the slope and the two intercepts the X intercept and the Y intercept. Now, when it comes to finding these, one of the best places to start is to put our original equation and to into the slope intercept form, which has a reminder is why equals M X plus B. The reason why this format is so helpful here is because M is the slope of my line and the B gives me my Why intercept. Now remember, the Excel I intercepts are both points. The Y intercept has an X value of zero. The X intercept has a Y value of zero. So we're looking at the B in our equation here. That's really the Y. Coordinate of the Y intercept is how we would look at that. So let's go back to our original equation and see if we can put it into slope intercept form. So I'm going to solve it for why everything That's not a while put to the right hand side, So that leaves negative four wide on the left. And when I subtract 16, that gives me 19 on the right. Now I'm going to divide both sides by negative four, and I get why equals negative 19 over four? Well, let's take a look at that. In terms of slope intercept form, there is no X here, which makes this. I could actually kind of rewrite this as zero X minus 19/4, which makes it a little clearer that are slope is zero. So this slope, this has zero slope. It just is a Y value that is a horizontal line. And it's that horizontal line at why equals negative 19 4th. So where is our Y intercept? Well, that's that. That's that constant term here. So that means my Y intercept is at zero negative 19 4th. But what about the X intercept? Well defined the X intercept and go back to my original equation, and I'm going to substitute in a zero for why and then solve for X. But the problem is, when I do that, I get 16 minus zero, which is 16 equals 35. That can't happen, so there is no X intercept, which makes sense if I have a horizontal line, any horizontal line. If here's my coordinate system, no matter where I place that line in this case, it's about negative. 19 4th that's down here. Yeah, it's not ever going to cross. The X axis is either going to be below it forever in either direction. Or if it's up here, it's gonna be above the X intercept forever in either direction, and it will never actually cross, So there is no X intercept for this line.

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