Find the slope and y-intercept of each line, and graph it. x+2y =...

Question

Find the slope and y-intercept of each line, and graph it. x+2y = -4

Accepted Answer

Hello everybody. I have everything. All right today today we're gonna be looking at this math question that says determine the Y intercept and the slope of the line defined by the following equation. Then graph the line. Now the equation given to us is 15 X minus 60 Y is equal to negative 42. Now source A is a graph with a slope of 1/4 and A Y intercept at negative seven divided by 10 with points at zero comma negative 7/10 divided by 10. And another point at 14 divided by five comma zero B is a graph with a slope of negative 1/4 and A Y intercept at negative seven divided by 10 with points at negative 14 5th comma zero and zero. Comma negative 7/10 C is a graph with a slope of 1/4 and A Y intercept of 7/10 and points at negative 14 5th comma zero and zero comma 7/10 N D is a graph with a slope of negative 1/4 and a set of 7/10 with points at zero comma 7/10 and 14 5th comma zero. Now, the first thing we we can do with this is look at our equation and see how we can manipulate it. So we know that the line equation is Y equals M X plus B, right, Y equals M X plus B where M is the slope and B is the Y intercept and Y and the X are just points values for those points. So let's try to manipulate our equation to get there. So we wanna get the Y on one side. So we'll have negative 60 Y is equal to negative 42 minus 15 X. Now we multiply everything by negative one, we have 60 Y is equal to and now it would be positive plus 15 X and now we can do some rearranging just to have everything the way we want it. 60 Y equals 15 X. We'll put first plus 42 and now we can divide both sides by 60. So we'll have Y is equal to 15/60 or divided by X plus 42 divided by 60. Now, with this equation, we can do some simplification. So we'll have Y is equal to 15 or divided by 60 can be simplified as one divided by four X plus. And now we can divide the 42 the 60 by six. So we'll have seven divided by 10. So our line equation will be Y equals 1/4 X plus 7/10. Now the 1/4 is the M and the Y equals M X plus B and recall that M equals slope and B equals Y intercept. So in this case, we'll have a slope of 1/ and A Y intercept of seven 10th. And we obtain that just from looking at the equation that we have. So let's see our answer choices. We see that answer choice A has a slope of 1/4 with which is what we have but what, but A Y intercept of negative 7/10 which is not what we have. Answer choice B is a slope of negative 1/4 and we have positive 1/4. So once again, that does not match with our answer. C has a slope of 1/4 and a wide set of 7/ which checks out with what we have. D has a slope of negative 1/4 which is not what we have. So we can shift our attention to answer to C and I'll cross out A B and D so we can focus on answer choice C so we can verify the points that they gave us by doing some plugging in. Now to do that, we can just plug in a zero for the X, solve for that Y and A zero for the Y and solve for that X. Now if you plug in a zero for the X, that'll be a Y intercept. And we already have the Y intercept which is 7/10. So we'll have a Y intercept of zero comma 7/ which is one of the points given to us. Now, let's check out the X intercept, which is the other point that they gave us. So to do that and we'll write X intercept to do that. We'll plug in zero for the Y. So we'll have zero is equal to 1/ X plus seven tense. Now, first, we'll move that 7/10 over from the right hand side to the left hand side. So we'll have negative 7/ equals 1/4 X and now we'll move that 1/4 over. So we'll have negative seven tense divided by 1/4 equals X and negative 7/10 divided by 1/4 is the same as saying and let me just scroll down a bit just to have more room to work with negative 7/10 divided by 1/4 is the same as saying, negative seven divided by 10, multiplied by four, divided by one and that's equal to X. So we'll have negative 28 divided by 10 which simplifies as negative 14, divided by five. And that will be equal to X or the point negative 14 fifths comma zero, which once again is confirmed in our graph and is one of the points given to us. So we can now confidently say that answer choice C is the answer to our question and the graph matches the graph that we need. So I hope that was helpful and until next time.

Find the slope and y-intercept of each line, and graph it. x+2y = -4

Key Concepts

Slope-Intercept Form

Slope

Y-Intercept

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