Answer:
B) Both functions have a y-intercept of -2.
Step-by-step explanation:
Hi there!
A) Both functions are always increasing.
⇒ False
Let's first take a look at the given equation, [tex]y=3x-2[/tex]. This is a linear equation, and it is organized in slope-intercept form: [tex]y=mx+b[/tex]. m is the slope and b is the y-intercept. When m is positive, it is always increasing.
In [tex]y=3x-2[/tex], 3 is m, and because it's positive, this line is always increasing on a graph.
However, when we take a look at the given graph, this isn't the case. It is decreasing for values of x below 0 (on the left side of the y-axis).
B) Both functions have a y-intercept of -2.
⇒ True
In the given equation [tex]y=3x-2[/tex], this is true. -2 is the y-intercept.
On the given graph, we can see that the graph intercepts the y-axis at -2, so this is also true for the graph.
C) Both functions are symmetric about the y-axis.
⇒ False
The given graph is symmetric about the y-axis, but the line is not. Any line that would be symmetric about the y-axis would be in the form [tex]y=b[/tex], which isn't the case here with [tex]y=3x-2[/tex]. [tex]y=3x-2[/tex] has a slope.
D) Both functions are linear relationships.
⇒ False
Sure, [tex]y=3x-2[/tex] is a linear equation, making it a line, but not the given graph. The graph does not resemble a straight line, so it is not a linear relationship.
I hope this helps!
