In Exercises 46–49, give the slope and y-intercept of each line w...

Question

In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line. 2x + 3y + 6 = 0

Accepted Answer

Welcome back. I am so glad you're here. We are given this line negative four X plus two, Y minus one equals zero. And we have to find the Y intercept and the slope of the that line. And then we need to graph that line. So we've got several things to do here. Well to determine the slope and the Y intercept. We recall from previous lessons that we can change that line into slope intercept form which is Y equals M. X plus B, where M equals the slope and B equals the Y intercept. So let's rearrange our equation so that it looks like Y equals M. X plus B. So let's move our X. And our constant term over to the right hand side so that the Y is by itself on the left will add four X to both sides and add one to both sides. So we'll have two. y equals four x plus one. And now that Y has to be completely by itself. So let's defied everything by two. And then we'll have Y by itself on the left, Y equals and four divided by two is two. So we have two, X plus and one divided by two is one half. So our slope R. M, which is right in front of the X. R. M is equal to two. And our B. The constant term here on the end, the y intercept equals one half. So what does that mean that our Y intercept equals one half. That means that on our graph the line is going to intercept with the Y axis at zero for the X. Value and one half for the Y value. So let's graph that we have a vertical Y axis and a horizontal X axis. They meet together at the origin in the middle and we'll graph the Y intercept that will be at zero for the X. Value. And then going up one half for the positive one half for our Y value. So right here at zero one half is our Y intercept. Now let's graph a couple more points. We know that the slope is two. What does that mean? So too is the same as 2/1. And we recall that this is the rise over the run. So it'll be going up two units and to the right one unit. So the X value from before zero gets one added to it. So that will be one and the Y value. One half gets to added to it or four halves. So that will be five halves. And then let's plot one more point. So we're going to be going up to again for ry for our rise and over to the right one for our X value. So we're adding one to our X one plus one is two and adding to to ry five halves plus two is nine halves. And we can connect these dots and we've got our line. All right. Now we need to look at our answer choices and determine which one matches. So we've got a slope of two. Well, that is correct here. For answer choice A in a y intercept of one half. Well, that is also correct. And look at these points on this graph. They have 01 half and they have to nine halfs. We'll answer choice A looks good. Let's just check the other three really quick. We're looking for it. Let's look for a slope of two. We'll be already has a slope of one half that one doesn't work. See slope of 1/2 that one doesn't work. And d's slope is negative two, yep. We have the correct answer choice with answer choice. A Well done. We'll catch you on the next one.

In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line. 2x + 3y + 6 = 0

Key Concepts

Slope-Intercept Form

Finding the Slope

Graphing Linear Equations

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