Perpendicular line always have slopes that are negative reciprocals of one another. Mathematically,

m1*m2=-1

So to be perpendicular to the line given, let's rearrange it to the point slope form of a line...

3y=6x ?3 (not sure what you wanted to type there)

anyway isolating y by dividing both side by three will leave 2x where 2 is the slope.

So for the other line to be perpendicular, m*2=-1, m=-1/2, now we have:

y=-x/2 +b, we can now you the point given to solve for b

4=-2/2 +b

4=-1+b

b=5 so

y=-x/2 +5 or more neatly

y=(10-x)/2

3 0

3 years ago

The rate of change in the function y=x+4 is________ the rate of change of the function represented in the table.

Snezhnost [94]

Recall that the slope is the "average rate of change" of any function.

$\bf y=\stackrel{slope}{1}x+4\qquad \qquad 
\begin{array}{ccll}
x&y\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
0&6\\2&8\\4&10\\6&12
\end{array}
\\\\\\
\textit{let's check what is the slope of the tabled function}\\
\textit{by using two points from it}$

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 2}}\quad ,&{{ 8}})\quad 
% (c,d)
&({{ 6}}\quad ,&{{ 12}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{12-8}{6-2}\implies \cfrac{4}{4}\implies 1$

4 0

4 years ago

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