Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (1,3), m = -2

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Accepted Answer

Hello everybody. I'm doing all right. Today, today we're gonna be looking at this math question that's telling us to find the equation of a line passing through the 0.5 comma eight and having a slope M equal to negative six and to write the equation in the standard form. Now the answers provided are a six X plus Y equals B six, X plus Y equals negative 38 C six X minus Y equals to 38 or D six X minus Y equals negative 38. Now, when looking at a question like this, I see they gave us a point that the line passes through and the slope of the line and they want this in standard form. So what to do that? We're gonna use an equation called the point slope form. And I'll write the equation for that. That will be Y minus Y one is equal to M and being the slope multiplied by X minus X one here. Why one will be equal to the Y and R point? So A and X one will be equal to the X in our point. So five. So in this case, we have five and eight. But if they were giving us another point, you can just plug in the X and the Y given for that point or X one, N Y one, you do not plug it in for the Y alone or the X alone. It has to be for Y one and X one. So let's do that plug in. So we'll have Y minus Y one, which is eight in our case equals M and they gave our slope of M. So we'll have negative six multiplied by X minus X one, which in our case is five. And now we can distribute and we'll have Y minus A is equal to negative six, multiplied by X is negative six X and they'll have negative six multiplied by negative five, which will be positive 30. So we'll have plus 30 and now it's all about getting the same like terms on the same side. So we want the variables on one side and the numbers on the other on the other side. So we can move the six X over from the right hand side to the left hand side and the ne the minus eight from the left hand side to the right hand side. So we'll have Y plus six X equals plus 30 plus eight. So we can just do some rearranging now and we'll have six X plus Y is equal to 30 plus eight, which is 38. And that will be the standard form for our equation or in this case, answer choice. A so I hope that was helpful. And until next time.

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (1,3), m = -2

Verified Solution

Key Concepts

Point-Slope Form of a Line

Slope-Intercept Form

Standard Form of a Line