Graph the line passing through the given point and having the ind...

Question

Graph the line passing through the given point and having the indicated slope. Plot two
points on the line. See Example 7. through (3, -4), m = - 1/3

Accepted Answer

Hello everybody. I have been doing all right today. Today we're gonna be looking at this math question that's telling us that a line has a slope of negative eight divided by nine and passes through the 0.9 comma negative one and identify two points and graph this line. Now, the answer choice providers provided show us four different graphs with answer choice A being a line that's angled upwards passing through the points zero, comma negative nine and nine comma negative one. B is a line angled downwards passing through the 10.0 comma three and nine comma negative one. C is a line angled upwards passing through the 0.0 comma negative five and nine comma negative one and D is a line angled downwards patterns passing through the points zero, comma seven and nine comma negative one. Now, they tell us that our line has a slope of negative eight divided by nine. So what does this mean? Well, slope is equal to the change in Y. So delta Y divided by the change in X. So delta Y over delta X. And another way to think about this and commonly written is that it is also equal to the rise divided by the run. So when you think about rise, it's just how you move up and down along a graph. And the run is how much are you moving to the right or to the left? Now, if you have a negative slope, that means that one, either the numerator or the denominator are negative. So if you have a negative rise, you're going downwards right? And then you have, you can't have a negative rise and a negative run because then you would have a positive slope once again. Therefore, you need to have, let's say a negative rise, meaning you go downwards and a positive run, meaning you go to the right. So you go downwards and you're changing Y and to the right and you're changing. Therefore, that will give you a line that's angled downwards. So we can right away eliminate answer choices. A and answer choices. C because both of those lines are angled upwards, meaning that they're gonna have a positive slope since their rise is positive, moving upwards and their run is also positive, moving to the right. So from here we can go a couple of different routes. We can use the slope that they gave us to visualize the changes in the points. Since our answer choices have points already provided and given to us, we can just use the slope to visualize it, visualize this if they didn't. And we wanted to test other different points. We would have to go through different formulas to give us a line equation. And to do that, you want to write and use what is called as point slope form. And I'll write, I'll go briefly through how to do this. But I will ultimately be using the visualization strategy of using the slope. So points look form is a formula that basically states Y minus Y one with Y one being the Y and the point given in this case negative one and that'll be equal to M which is the slope multiplied by X minus X one which is once again X one being the X of the point given in this case nine. So we would have Y minus Y one equal to M multiplied by X minus X one. So in this case, you would plug in the slope that they provided us and the point that they provided us for Y one and X one and solve for Y and you would come to the conclusion of an equation in the form of Y equals M X plus B. And now this is the gen the general line equation where the Y is just the Y of a point, the X is the X of a point. The M once again is the slope and the B is the Y intercept to solve for B, you just plug in zero for X and then solve for why in that value of Y it would be the B because it's the X, the Y intercept. And once you have that formula with the slope and the Y intercept, you can try different points to see if the formula fits that point. And if it does, then you know your line passes through that. However, in this case, since they give us points, I'm just gonna be using the slope to visualize the line. So the slope is negative eight divided by nine. And we know that's rise over run, which means we go down eight and to the right nine. Now let's look at answer choice B if we start at the 0.0 comma three that they gave us and we go down eight. So our initial Y is three and now we go down eight, we'll be at negative five A Y of negative five. However, the Y of the next point that they give us is negative one. So those don't align. Therefore, we can eliminate answer choice B now we go to answer choice D it's the only one remaining but we have to check if it's, if it works for this one. So we start at a point of zero comma seven and our Y being seven. So we go down eight. So we would be at a Y of negative one which matches the point that they gave us. So now we check the X, we go to the right nine and we started at zero. So now we would be at nine comma negative one, which is exactly the point that they gave us. So that confirms that answer choice D would be the answer to this question. So I hope that was helpful. And until next time.

Graph the line passing through the given point and having the indicated slope. Plot two points on the line. See Example 7. through (3, -4), m = - 1/3

Key Concepts

Slope-Intercept Form

Point-Slope Form

Graphing Linear Equations

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