Which of the following points would fall on the line produced by the point-slope form equation y + 4 = 2(x - 3) when graphed?
plug the points into the equation to test if they lie on the line
To determine which points would fall on the line produced by the given equation in point-slope form, we need to substitute different values of x and solve for y.
The given point-slope form equation is: y + 4 = 2(x - 3)
Let's solve for y by isolating it on one side of the equation:
y + 4 = 2(x - 3)
y + 4 = 2x - 6
y = 2x - 6 - 4
y = 2x - 10
Now we have the equation in slope-intercept form: y = 2x - 10
To find the points on the line, we can substitute different x-values into the equation and calculate the corresponding y-values.
For example:
If we let x = 0, then y = 2(0) - 10 = -10, giving us the point (0, -10).
If we let x = 2, then y = 2(2) - 10 = -6, giving us the point (2, -6).
If we let x = -3, then y = 2(-3) - 10 = -16, giving us the point (-3, -16).
Therefore, the points (0, -10), (2, -6), and (-3, -16) would all fall on the line produced by the given equation when graphed.