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Paraphin [41]
3 years ago
11

What is the slope of the line with equation y=12x

Mathematics
1 answer:
fomenos3 years ago
5 0
  <span>When you have an equation of the form y = mx + b (which you do in this case), the slope is always equal to the coefficient of x, which is m or 12 in this case. Since there is no "b" in your equation, you could say that b=0, and the line is known to cross the y axis at zero. 

In case you are interested, if the equation said y = 12 x + 3 the slope of the line would still be 12 but the line would cross the y axis at 3. If the equation said y = 12x -4, the line would have a slope of 12 and would cross the y axis at -4.</span>
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well, about A and D, I just plugged the values on the slope formula of

\bf \begin{array}{llll} g(x)=x^3-4x+1\\ L(x) = 8(x-2)+1 \end{array} \qquad \begin{cases} x_1=1.9\\ x_2=2.1 \end{cases}\implies \cfrac{f(b)-f(a)}{b-a}

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for D the values are -2.25 and 8.0, so no dice on that one.

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checking L(x) y-intercept, well, L(x) is in slope-intercept form, thus the +1 sticking out on the far right is the y-intercept, so, dice. \textit{\huge \checkmark}

for C, well, the slope if L(x) is 8, since it's in slope-intercept form, the derivative of g(x) is g'(x) = 3x² - 4, and thus g'(0) = -4, so no dice.

for E, do they intercept at (2,1)?  well, come on now, L(x) is a tangent line to g(x), so that's a must for a tangent. \textit{\huge \checkmark}

for F, we know the slope of the line L(x) is 8, is g'(2) = 8?  let's check

recall that g'(x) = 3x² - 4, so g'(2) = 3(2)² - 4, meaning g'(2) = 8, so, dice. \textit{\huge \checkmark}

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