Given the linear equation y = 4x + 2, find the y-coordinates of the points (-2, ), (1, ), and (-3, ). Please show all of your work. Plot these points and graph the linear equation.
To find the y-coordinates of the given points (-2, ), (1, ), and (-3, ) in the equation y = 4x + 2, we need to substitute the given x-values into the equation and solve for y.
For the first point (-2, ), we substitute x = -2 into the equation:
y = 4(-2) + 2
y = -8 + 2
y = -6
So the y-coordinate for the point (-2, ) is -6.
For the second point (1, ), we substitute x = 1 into the equation:
y = 4(1) + 2
y = 4 + 2
y = 6
So the y-coordinate for the point (1, ) is 6.
For the third point (-3, ), we substitute x = -3 into the equation:
y = 4(-3) + 2
y = -12 + 2
y = -10
So the y-coordinate for the point (-3, ) is -10.
Now, let's plot these points on a graph. The x-coordinates are -2, 1, and -3, and the y-coordinates are -6, 6, and -10.
Plotting the points: (-2, -6), (1, 6), and (-3, -10), we get the following points on the graph:
|
| o (1, 6)
|
| o (-2, -6)
|
| o (-3, -10)
|_____________________________________
Next, let's graph the linear equation y = 4x + 2.
To graph the equation, we only need two points. Let's choose (0, ) and (2, ).
For x = 0:
y = 4(0) + 2
y = 0 + 2
y = 2
So we have the point (0, 2).
For x = 2:
y = 4(2) + 2
y = 8 + 2
y = 10
So we have the point (2, 10).
Plotting the two points (0, 2) and (2, 10), we get the following line on the graph:
|
|
| o (-2, -6)
|
| o (-3, -10)
| |
| o (0, 2) o (2, 10)
|_____________________________________
This line represents the linear equation y = 4x + 2.
to get the y-coordinates, we just substitute the value of the x-coordinates given.
at x = -2:
y = 4x + 2
y = 4(-2) + 2
y = -8 + 2
y = -6
thus (-2, -6)
at x = 1:
y = 4x + 2
y = 4(1) + 2
y = 4 + 2
y = 6
thus (1, 6)
at x = -3:
y = 4x + 2
y = 4(-3) + 2
y = -12 + 2
y = -10
thus (-3, -10)
to plot this, you locate all the points we solved above. then connect these points and extend on both ends.
hope this helps~ :)