Answer:
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b)\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\=============================[/tex]
[tex]f(x):\\\\given:\ (-1,\ -5),\ (0,\ -1),\ (1,\ 3)\\\\m=\dfrac{3-(-5)}{1-(-1)}=\dfrac{8}{2}=4\\\\(0,\ -1)\to b=-1\\\\f(x)=4x-1\\\\---------------------------\\\\g(x)=2x-7\to m=2,\ b=-7[/tex]
Answer:
Part A: The slope of F(x) is greater than the slope of g(x)
Part B: The Y-intercept of f(x) is greater than that of g(x)
Step-by-step explanation:
To calculate the slope on f(x) we just have to take two points from the table and use the formula for slope:
[tex]m=\frac{y^{2} -y^{1} }{x^{2}- x^{1} }[/tex]
Now the points to use will be:
P1:(0,-1)
P2:(1,3)
Now we just put this values into the formula:
[tex]m=\frac{y^{2} -y^{1} }{x^{2}- x^{1} }[/tex]
[tex]m=\frac{3-(-1) }{1- (0)} }[/tex]
[tex]m=\frac{4}{1}\\ m=4[/tex]
Now to know the slope of g(x) we just have to remember that in the function form y=mx+c the "m" represents the slope, so if g(x)=2x-7 the slope would be "2".
Now we know that f(x) has a greater slope.
To know the greater Y intercept we just take the point in the table where x is "0" since it´s where the Y intercepts with the Y axis, and in f(x) that point is (0,-1), now in g(x) we just evaluate the function to x=0.
[tex]g(x)=2x-7\\g(x)=2(0)-7\\g(x)=-7[/tex]
The Y intercept in g(x) would be in (0,-7), since -1 is greater than -7, we can say that f(x) has the greatest Y-intercept.
