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 (-2, 8), m = 2/5

Accepted Answer

Hello everybody. Uh We're doing all right today, today we're gonna be looking at this map question that tells us that a line has a slope of seven divided by 12 and passes through the point of negative 12 comma six and to identify two points and graph this line. Now the extras provided give us four different graphs with letter A being a line angled upwards passing through the point negative 12 comma six and zero. Comma 13 B is a line angled downwards passing through the point negative comma six N zero comma negative one C is angled upwards, passing through the points negative 12 comma six N zero comma and D is aligned angle downwards passing through the point negative 12, comma six and zero, comma zero. Now, the slope that they give us is seven divided by 12. So what is slope? Well, slope is equal to the change in Y. So delta Y divided by the change in X or delta X and this is more commonly written as rise divided by run. So when you think about rise and rising, you're thinking about moving upwards and downwards. So that's why it's the change in Y. And when we think about running, you can move from left to right in one direction horizontally. Therefore, that is the change in the X. So to have a positive slope like the one they gave us seven divided by 12, we can have a positive rise and a positive run. So a positive rise is moving upwards and a positive run is moving to the right. And if you connect those two directions, you will have a line angled upwards. So right away, we can eliminate answer choices B and answer choice D and we're left with A N C. Now we have a point given to us and a slope, we see that as choice A and ch choice C both pass through their point negative 12 comma six but have a different Y intercept A having zero comma 13 and C having zero comma 12. So we can make an equation for our line in the form of Y equals M X plus B. This is the general equation for our line. And now B is the Y intercept M is a slope, Y is the Y of our, of a point and X is the X of a point. So to sol for B, in this case, we can plug in the slope that was given to us as well as the point that was given to us and see what the B is. So let's do exactly that the point that was given to us has a Y of six. So six is equal to M which is the slope and that is equal to seven divided by 12, multiplied by X which is negative 12 in the point that was given to us plus B. So we look at that we have seven divided by 12 multiplied by negative 12. So because we have set 12 in the denominator of a fraction and when you multiply that by negative 12, that 12 is gonna cancel out and will be left with a negative. So we would be, it would be six equal to negative seven plus B and then you can move that seven over and add it to the six. So we will be left with 13 is equal to B this means that 13 is our Y intercept or zero comma 13 which is a point that matches with answer choice. A. So answer choice A will be the answer to our 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 (-2, 8), m = 2/5

Key Concepts

Slope-Intercept Form

Point-Slope Form

Graphing Linear Equations

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