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 twopoints on the line. See Example 7. through ( - 1/2 , 4), m = 0

Accepted Answer

Hello everybody. I hope you're 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 zero and passes through the point negative 3/5 comma 11 and identify two points and graph this line. Now the answer choices that provide us are all graphs with answer choice A being a horizontal line that passes through the points negative 3/5 comma negative 11 and zero comma negative 11 as choice B is the same as A but the Y values are positive C is a vertical line passing through the points negative 11, comma negative 3/5 and negative 11 comma zero and D is the same as C but with the X values positive. Now, the first thing we got to look at is they tell us that we have a slope of zero. So what exactly does this mean? What is slope? Well, slope is equal to the change in Y. So delta Y over the change in X. So delta X now to have a slope of zero, we set this equation equal to zero. So delta Y over delta X equals zero and how can you have a division equal to zero? Well, if you have the delta Y equal to zero, then the answer will be zero because zero, divided by anything is zero. Therefore, if delta Y equals zero, then slope equals zero. So what does delta Y equal to zero mean why means there's no change in Y if there's no change in Y, that means that the line must be horizontal because it doesn't move up or down. So it must be a horizontal line. Therefore, we can eliminate answer choices C and D right away. Now they tell us that this line passes through the point negative 3/5 comma 11. And as a choice A says negative 3/5 comma negative 11. But as choice B says negative 3/5 com positive 11, which is the number they told us the point they told us. And because it is a horizontal line, you can pick any point along that X along the X. If this is imagine this is an infinite line, you can pick any point along the X as long as it's on that Y value of 11 and it'll pass through that point and just to double check and make sure that this is correct. We can use something called the point slope form. So I'll write that just to get the math of it. So point slope form. So what is that? Well, we have a formula that says Y minus Y one is equal to M M being the slope of X minus X one. And now for Y one and X one, we plug in the values that we have and we know the slope is zero. So we can plug in for M. So we'll have Y minus Y one, which is 11 because the point they gave us was negative 3/5 comma 11, our slope is zero. So Y minus 11 equals zero, multiplied by then we'll have X minus X one, which in our case is negative 3/5. So it'll be plus 3/5 because you have minus a negative number. Now, when you multiply zero times X plus 3/ 0 times anything or multiple zero multiplied by anything is zero. So that will cancel out. So you will have Y minus 11 is equal to zero. Therefore, Y equals 11. So that confirms that the line will pass through the 0. comma 11 like an answer choice. B therefore, we can be confident in choosing answer choice B as our answer for this question. I hope that was helpful. And until next time.

Graph the line passing through the given point and having the indicated slope. Plot twopoints on the line. See Example 7. through ( - 1/2 , 4), m = 0

Key Concepts

Slope-Intercept Form

Slope

Plotting Points

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