What is the equation of the line that passes through the points and (1/2, -1/3) 2,2/3)

Mathematics

1 answer:

Readme [11.4K]4 years ago

6 0

Answer:

the desired equation is y = (2/3)x - 2/3

Step-by-step explanation:

As we go from (1/2, -1/3) to (2,2/3), x increases by 3/2 and y increases by 1. Hence, the slope of this line is m = rise / run = 1/(3/2), or 2/3.

Use the slope-intercept form of the equation of a straight line, y = mx + b:

Substituting 2/3 for y, 2 for x and 2/3 for m, we get:

2/3 = 2(2/3) + b.

Clear out the fractions by multiplying all three terms by 3:

2 = 4 + 3b, or -2 = 3b, or b = -2/3.

Then the desired equation is y = (2/3)x - 2/3

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erastova [34]

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$\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2}\implies \cfrac{3}{2}}}$