SOLUTION: Sketch the lines through the point with the indicated slopes on the same set of coordinate axes. (4, 2) (a)0 (b)1 (c)4 (d)−2

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Question 1196836: Sketch the lines through the point with the indicated slopes on the same set of coordinate axes.
(4, 2)
(a)0
(b)1
(c)4
(d)−2
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Part (a)

A slope of 0 means the line is completely horizontal. It doesn't go up or go down. There's no change in y value
slope = rise/run = 0/1 = 0
rise = change in y
run = change in x.

So if you wanted a line with slope 0 to go through (4,2) then it would also go through (3,2). Pick any x value you want, but the y value must be 2. All points on this line are of the form (x,2).

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Part (b)

A slope of 1 means 1/1
slope = rise/run = 1/1 = 1
rise = 1
run = 1
In this case we go "up 1, to the right 1"
If you started at (4,2) then you'd get to (5,3)

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Part (c)

Similarly a slope of 4 means 4/1
rise/run = 4/1 = 4
rise = 4
run = 1

So we go from (4,2) to (5,6) as the two points on this line.

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Part (d)

Lastly a slope of -2 = -2/1 means
rise = -2
run = 1
We go down 2 then to the right 1
Therefore we move from (4,2) to (5,0)

When graphing straight lines, we only need two points at minimum.

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