Question

consider the following equations:
y = x - 2
y = 2x - 2
y = -x - 2
y = -2
discuss the similarities and difference in the graphs of these equations. (use a graphing calculator if needed.)
a. same slopes; different y-intercepts
b. same slopes; same y-intercepts
c. different slopes; same y-intercepts
d. different slopes; different y-intercepts
please select the best answer from the choices provided
a
b

Explanation:

1. Recall the slope - intercept form of a line \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.
2. For the equation \(y=x - 2\), the slope \(m_1 = 1\) and the \(y\) - intercept \(b_1=-2\).
3. For the equation \(y = 2x-2\), the slope \(m_2 = 2\) and the \(y\) - intercept \(b_2=-2\).
4. For the equation \(y=-x - 2\), the slope \(m_3=-1\) and the \(y\) - intercept \(b_3=-2\).
5. For the equation \(y=-2\) (which can be written as \(y = 0x-2\)), the slope \(m_4 = 0\) and the \(y\) - intercept \(b_4=-2\).
6. We can see that the slopes (\(1\), \(2\), \(-1\), \(0\)) are different, but the \(y\) - intercepts (all \(-2\)) are the same. So the correct option is c.

Answer:

c. Different slopes; same y - intercepts