In Exercises 59-66, a. Rewrite the given equation in slope-int...

Question

In Exercises 59-66, a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. 4x+y-6=0

Accepted Answer

Welcome back. I am so glad you're here. We are given this linear function, we're given the equation of a line. It's one half X plus seven Y plus one equals zero. We are asked to write this in slope intercept form and then to graph it. So let's get that into slope intercept form. We recall from previous lessons that slope intercept form is in the format of Y equals MX plus B where M is our slope and B is our Y intercept. So getting this into slope intercept form essentially means we just want to get Y by itself on the left hand side of the equation, well, Y is already on the left hand side of the equation. So let's start moving the other things to the right, let's subtract one from both sides of the equation and we can subtract one half X from both sides of the equation. So on the left we'll have seven Y and that will equal negative one half X minus one. Now to get that Y by itself, we sub or excuse me, not subtract, we will divide everything by seven. So on the left we have Y by itself, ya, it's so happy. We have negative one half divided by seven. We could rewrite that as negative one half divided by seven, which is the same as negative one half times 1/7. Doing that multiplication in the numerators, that's negative one and the dominators that's 14th. So in front of the X, that's negative 1/14 and then minus 1/7. And there we have this in slope, Y intercept form our slope. The number right in front of the X is negative 1/14. Our Y intercept the B is at negative 1/7. OK. Now we just need to graph this. I'm giving myself a little bit more room going to draw a rough sketch of a coordinate plane. We have a horizontal X axis, a vertical Y axis and now our Y intercept is at zero for our X value and negative 1/7 for our Y value. So that's gonna be very close to zero. But we'll draw this from the origin 00. We're going neither left nor right for our X value and we're going down 1/7 for negative 1/7 and we'll label this as zero, negative 1/7 for our Y intercept. And for our slope, what we're doing here is we are going down, we have rise over run for this negative 1/14. So we're going down one unit for our Y value and we're going to the right 14 units for our X value. So down one to the right 14 for our X value that's going to look something like this. And we could also take it in the other direction if we wanted to have another point going the other way. So in this case, we would go up one unit, this would be like one negative 14th. So this would be going up one unit for our Y value and to the left 14 units for our X value. And that would look something like this. So our line would look like this. All right. So that is our linear function. And now we need to find the corresponding answer choice. Let's go back up and look at answer choice. A all right answer choice A, they had a slope of 14. No, we've got a slope of negative 1/14 and we have a Y intercept at negative 1/7. So answer choice A and that graph doesn't look right. That's not gonna work. Now, let's look at answer trace B that looks pretty similar. They've got a slope of negative 1/14 and they've got a Y intercept A B of negative 17 and that graph looks great. All right. Let's just rule out C and D um answer choice. Let's bring this down. Answer choice C has a slope of negative 14. Nope, that's not going to work in answer choice D they have a slope of 1/14 not negative 1/14. So answer choice B is the winner. Well done. We'll catch you on the next one.

In Exercises 59-66, a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. 4x+y-6=0

Key Concepts

Slope-Intercept Form

Slope of a Line

Graphing Using Slope and Y-Intercept

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