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. 4x + 3y = 12

Accepted Answer

Hello everybody. Everything. All right. Today, then we're going to be looking at this question that states determine the slope of the given line and plot it on the rep recording system where the equation power line is 18 X plus 17 Y equals 306. Now for an equation like this, where they asked me to determine the slope. The first thing I wanna think about is how can I determine that from the equation that we have? And I can recall that there is something called slope point form for align, which is a way to write the equation of the line that will tell us the slope the Y intercept and will allow us to plug in any points that we would like. So the general formula for that is Y equals M X plus B where M equals slope and B equals why intercept? So let's try to manipulate our equation to get it into this form. So like I said, we have 18 X, so we have 18 X plus 17 Y equals 306. Now, if we move the 18 X over from the left hand side to the right hand side, we'll have 17 Y equals and I'll place the 18 X first so that it's matches the form that we want. And if we had a positive 18 X on the left hand side, now we'll have a negative 18 X on the right hand side. So we'll have negative 18 X plus 306. And now to isolate the Y, we can divide both sides by 17. So we'll have that Y equals negative and then we'll have a fraction in the, in the numerator. We have 18, X plus 306 divided by 17. And that can be simplified into having Y equals negative 18, divided by 17 X plus. And we'll have 306 divided by 17, which is 18. So the equation for our line is going to be Y equals negative 18 divided by X divided by 17, multiplying X plus 18. Now, comparing that to the general formula that we had Y equals M X plus B. We see that M oh, we'll write that slope equals M equals negative 18 divided by 17. Because that's what the term in front of the X. So we can see that we have a negative slope, meaning our line will be inclined downwards. Now are Y intercept equals B which equals 18. And to put that as a point, we'll have zero comma 18 because the Y intercept is when we intersect the Y axis, meaning our X value is zero. So now we can determine the X intersect. So we'll plug in 04 Y because once again, if we're intercepting the X axis, our Y value will be zero. So we plug in zero for the Y. So we'll have zero equals negative 18 divided by 17 X plus 18 and will move the 18 over from the right hand side to the left hand side to have negative equals negative 18 divided by 17, multiplying X. And now we can move the negative 18 divided by 17 to the right to the left hand side by mo by dividing. So we'll have negative 18. And if we divide negative that by negative 18, divided by 17, we're really multiplying by negative 17 divided by 18, which means our negatives will cancel and our eighteens will cancel and will be left with X equals 17 or a point at 17 comma zero. And that will be our X intercept. So now that we've obtained the slope, we have the Y intercept and the X intersect, we can go ahead and grab a general shape. So we draw a Y axis and an X axis and we'll plug in the points that we have. So we know that we had a Y intercept at zero comma 18. So we'll draw a dash on the Y axis and label it 18 and we'll put place a point there and then we'll draw on the X axis at point at 17, I will place a point there and then we can connect those two points and just gotta make sure that the points connect well. And then we can extend the graph past each point. Since we have a negative slope, we know that the line will be inclined downwards. So that is a general graph for our equation with a slope of negative 18 divided by 17 A Y intercept of zero comma 18 and an X intercept of 17 comma zero. 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. 4x + 3y = 12

Key Concepts

Slope of a Line

Graphing Linear Equations

Standard Form of a Linear Equation

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