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Please help!!

-1,-6
1,-2
3,2

write the equations of a liner function that had a y-intercept greater than the function represented in the table and is parallel to the function y+ 1/4x=2

Please help!! -1,-6 1,-2 3,2 write the equations of a liner function that had a y-example-1
User Kelsea
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1 Answer

8 votes

to get the equation of any straight line, we simply need two points off of it, so for the equation in the table, let'use the points in the picture below


(\stackrel{x_1}{1}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}}\implies \cfrac{2+2}{2}\implies 2 \\\\\\ \begin{array}ll \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{2}(x-\stackrel{x_1}{1})\implies y+2=2x-2


y=2x\stackrel{\stackrel{b}{\downarrow }}{-4}\qquad \impliedby \begin{array}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}

so the equation in the table has a y-intercept of -4.

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above


y+\cfrac{1}{4}x=2\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{4}} x+2\qquad \impliedby \begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}

so hmmm we're really looking for an equation whose slope is -1/4 and with a y-intercept greater than -4, hmmm let's recall something, that on the negative side of the number line, the closer to 0, the greater.

that said, on the negative side of the number line -10 is much larger than -1,000,000, because -10 is closer than -1,000,000 to 0, and so on.

so hmmm what's greater than -4? hmm well, heck let's use -2


y = -\cfrac{1}{4}x - 2

Please help!! -1,-6 1,-2 3,2 write the equations of a liner function that had a y-example-1
User David Murdoch
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