John drew a polygon with two line segments

Mathematics

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Leto [7]3 years ago

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A line, y = mx + b, passes through the point (10, 3) and is parallel to the line 2x+5y=12.

slava [35]

We have been given that a line $y=mx+b$ passes through the point (10, 3) and is parallel to the line $2x+5y=12$ . We are asked to find the y-intercept of the line.

First of all we will rewrite our given equation in slope-intercept form as:

$2x-2x+5y=12-2x$

$5y=-2x+12$

$\frac{5y}{5}=-\frac{2}{5}x+\frac{12}{5}$

$y=-\frac{2}{5}x+\frac{12}{5}$

We know that slope of parallel lines is equal, so slope of parallel line to our given line would be $-\frac{2}{5}$ .

Now we will use slope-intercept form of equation to find y-intercept.

$y=mx+b$ , where,

m = Slope,

b = The y-intercept.

Let us substitute $m=-\frac{2}{5}$ and coordinates of point $(10,3)$ in above equation as:

$3=-\frac{2}{5}(10)+b$

$3=-2(2)+b$

$3=-4+b$

$3+4=-4+4+b$

$7=b$

Therefore, the y-intercept is 7 and our required equation would be $y=-\frac{2}{5}x+7$ .

5 0

3 years ago

If p varies directly as q and q= 70 when p= 10, find q when p = 12

stellarik [79]

$\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill$

$\stackrel{\textit{"p" varies directly as "q"}}{p~~ = ~~kq}\qquad \textit{we also know that} \begin{cases} q=70\\ p=10 \end{cases}\implies 10=k70 \\\\\\ \cfrac{10}{70}=k\implies \cfrac{1}{7}=k\hspace{15em}\boxed{p=\cfrac{1}{7}k} \\\\\\ \textit{when p = 12, what is "q"?}\qquad 12=\cfrac{1}{7}q\implies 12=\cfrac{q}{7}\implies 84=q$