Question 1202654: Give three different points that lie on the line y=4x-5 by choosing different values for x.
Note that you must answer all three questions in order for you responses to be scored correctly.
Found 2 solutions by Edwin McCravy, math_tutor2020:
Answer by Edwin McCravy(20054)   (Show Source):
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
We can pick any number to replace x.
The idea is to find paired y values so we can generate (x,y) point locations.
Let's replace x with 0.
Use PEMDAS to simplify.
y = 4x-5
y = 4*0-5
y = 0-5
y = -5
The input x = 0 leads to the output y = -5.
The point (x,y) = (0,-5) is on the line. It is the y intercept.
Let's repeat similar steps for x = 1
y = 4x-5
y = 4*1-5
y = 4-5
y = -1
Therefore, the point (1,-1) is also on the line.
Now let's try x = 2.
y = 4x-5
y = 4*2-5
y = 8-5
y = 3
The point (2,3) is on the line.
These three points are on the line:
(0,-5)
(1,-1)
(2,3)
There are infinitely many other points, so feel free to explore alternative answers.
Refer to the graph the tutor Edwin had made.
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Another approach:
The equation y = 4x-5 matches up with y = mx+b known as slope-intercept form.
m = 4 = 4/1 = slope
b = -5 = y intercept
The y intercept is at (0,-5)
Apply the movement pattern of "up 4, right 1" to go from (0,-5) to (1,-1).
This movement pattern is directly connected to the slope and nothing else.
slope = rise/run = 4/1
rise = 4 = go up 4
run = 1 = go right 1
Then from (1,-1) move "up 4, right 1" again to arrive at (2,3)
Keep this movement pattern going to go from (2,3) to (3,7)
And so on.
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