For each line, (a) find the slope and (b) sketch the graph. See E...

Question

For each line, (a) find the slope and (b) sketch the graph. See Examples 6 and 7. 5x - 2y = 10

Accepted Answer

Hello everybody. Everything right today that we are going to be looking at this question that states determine the slope for the given line and plot it on the rectangular coordinate system where our given line has an equation of eight X minus three Y equals 27. Now, when going to solve this, I look at first look at the equation they gave us and I right away can see that we can rewrite this in something we call slope intercept form. And that's exactly what I'll do because this other formulas, the slope intercept form will give us information about the slope and the Y intercept. So this formula has a general way of being written as Y equals M X plus B where M equals slope and B equals Y intercept. So I'm going to try to manipulate the formula. We have the eight X minus three Y equals 27. And I'll try to manipulate it in a way that we can have the Y equals M X plus B form. So first, I'm going to move the Y to its own side. In this case, I'll move it to the right hand side of the equation and the 27 I'll move it to the left. So we'll have eight X and now we're moving the 27 from the right hand side to the left hand side and we had a positive 27. So now we'll subtract it. So we'll have eight X minus 27 equals. And now we had the three Y on the left hand side, which was negative. And if we move it to the right hand side, we'll be adding it. So we'll be equal to positive three Y. Now we divide everything by three to have the Y by itself. And we'll have that Y is equal to eight divided by three X minus nine. So that is the equation for our line. And with that information, we can see that R M is equal to eight divided by three. So our slope is eight divided by three and our Y intercept is the negative nine. The negative nine here functions or the minus nine would be a negative nine functions as the B. So the Y intercept is negative nine or a point at zero. Comma negative nine. No, we want to look for another point. And in this case, we'll look for the X intercept. And for that, we just have to plug in zero for our Y. So we'll have zero is equal to eight divided by three X minus nine. So I'll move the nine over from the right hand side to the left hand side and by adding, and we'll have that nine is equal to eight divided by three X. And then I'll move the eight, divide the three that's dividing, I'll move it over to the left hand side by multiplying by three. So nine multiplied by three is 27. So I have that 27 is equal to eight X. So now we have to divide both sides by eight and we'll have divided by eight is equal to X or a point at 27 divided by eight comma zero. That will be our X intercept. So now we have a slope, we have a Y intercept at zero comma negative nine and an X intercept at 27 divided by eight comma zero. So now we can do some graphing, we can graph a general idea of what our graph will look like. So we'll draw a Y axis and an X axis and we'll put eight points at negative nine on a, on a Y of negative nine. That's a Y intercept. And for our X intercept, we had 27 divided by eight, which is between three and four because eight times three or eight multiplied by three is 24 8, multiplied by four is 32. So 27 is between those numbers. So we'll have it between three. What will point out where the three could be and where the four could be and will note that our line will intersect somewhere in between those two points between the three and the four. And as we mentioned, we have a positive slope a divided by three. So we'll just connect those two points and continue the line upwards and downwards. And we'll label our points at, at zero, comma negative nine and at 27 divided by eight comma zero. And like that, we have obtained the slope of our line and have graphed a general idea of what it would look like on a rectangular coordinate system. So I hope that was helpful. And until next time.

For each line, (a) find the slope and (b) sketch the graph. See Examples 6 and 7. 5x - 2y = 10

Key Concepts

Slope of a Line

Graphing Linear Equations

Standard Form of a Linear Equation

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