D)The slope is -2/3
First, put this equation in slope-intercept form by subtracting 2x on both sides:
Your equation should be:3y=-2x+6
Then, divide the whole equation by 3 since y has to be by itself
Your equation should be y=-2/3x+6
Since the slope in slope-intercept form is m in y=mx+b, -2/3×=m
Final D) The slope is -2/3
the answer is d
Consider the function f(x)=2/3x+4 and the linear function g(x) represented in the table.
Which statement about the functions is true?
a.f(x) and g(x) have the same y-intercept.
b.The slope of f(x) is greater than the slope of g(x).
c.f(x) and g(x) have the same x-intercept.
d. The slope of g(x) is greater than the slope of f(x).
well, the y-intercept for f(x) is at
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.
whenever an x-intercept occurs, y = 0, for f(x) that's at
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.
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,
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.
well, you already know.