a)
well, the y-intercept for f(x) is at [tex]\bf f(x)=\stackrel{slope}{\cfrac{2}{3}}x+\stackrel{y-intercept}{4}[/tex]
as you can see from the slope-intercept form is at 4, and it has an slope of 2/3.
for g(x), well an y-intercept is when x = 0, what is it from that table? well, is at 0,3, so when x = 0, y = 3, so no dice on that one.
c)
whenever an x-intercept occurs, y = 0, for f(x) that's at
[tex]\bf 0=\cfrac{2}{3}x+4\implies -4=\cfrac{2}{3}x\implies -12=2x\implies -6=x[/tex]
what about the x-intercept for g(x)? well, let's check, when is y = 0? aha! at -9, 0, so when y = 0, x = -9, so no dice on that one either.
d)
well, what is the slope of g(x) anyway? well, let's pick two points off the table to get it hmmm the first two let's use,
[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -9 &,& 0~)
% (c,d)
&&(~ -6 &,& 1~)
\end{array}
\\\\\\
% slope = m
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-0}{-6-(-9)}\implies \cfrac{1-0}{-6+9}\implies \cfrac{1}{3}[/tex]
and from a), using the slope-intercept form, we know f(x) has a slope of 2/3.
well, 2/3 is larger than 1/3, so no dice.
b)
well, you already know.
