help Given the function f(x) = 4x + 10 and g(x), which function has a greater slope? x g(x) 2 5 4 7 6 9<

Question

help Given the function f(x) = 4x + 10 and g(x), which function has a greater slope?

x g(x)
2 5
4 7
6 9
f(x) has a greater slope.
g(x) has a greater slope.
The slopes of f(x) and g(x) are the same.
The slope of g(x) is undefined.

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Valentina 11 mins 2021-10-13T05:44:24+00:00 2 Answers 0

Answers ( )

    0
    2021-10-13T05:45:50+00:00

    Answer:

    f(x) has a greater slope.

    Step-by-step explanation:

    The slope of a function in the form of y=Mx+C is represented by the letter M, so the slope in the function F(x) =4.

    Now when you have a function but you only have a table to evaluate it, to calculate the slope you have the next formula:

    m=\frac{y^{2}- y^{1}}{x^{2} -x^{1} }

    You just have to pick two points from the table to use in the formula, we┬┤ll use (4,7) as our point 1 and

    (6,9) as our point 2.

    This means that:

    x^{1}=4 y^{1}=7

    x^{2}=6 y^{2}=9

    Now you just put it into the formula:

    m=\frac{9-7}{6-4}

    m=\frac{2}{2}

    m=1

    Now that you have both slopes, you can see that the slope of g(x)=1 and the slope of f(x)=4, and you can see that f(x) has a greater slope thatn g(x).

    0
    2021-10-13T05:46:19+00:00

    \bf f(x)=\stackrel{\stackrel{m}{\downarrow }}{4} x+10\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill

    \bf \begin{array}{ccll} x&g(x)\\ \cline{1-2} 2&5\\4&7\\6&9 \end{array}~\hfill \begin{array}{llll} (\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-5}{6-2}\implies \cfrac{4}{4}\implies \stackrel{\stackrel{m}{\downarrow }}{1} \end{array}

    well, clearly 4 > 1.

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