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Anna007 [38]
3 years ago
15

Complete the equation of the line through (2,-2)(2,−2)left parenthesis, 2, comma, minus, 2, right parenthesis and (4,1)(4,1)left

parenthesis, 4, comma, 1, right parenthesis. Use exact numbers.
Mathematics
1 answer:
Daniel [21]3 years ago
3 0

Answer:

y=\frac{3}{2}x-5

Step-by-step explanation:

There are a couple of ways to solve this, depending on what you already know.

Point-Slope Form

y-y_1=m(x-x_1)  where <em>m</em> is the slope and (x_1, y_1) is a point on the line.

First, calculate the slope using the two given points (x_1, y_1), (x_2, y_2).

m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-2)}{4-2}=\frac{3}{2} .

Fill in the point-slope pattern

y-(-2)=\frac{3}{2}(x-2) \\ y+2=\frac{3}{2}x-3 \\ y=\frac{3}{2}x-5

There's the equation in slope-intercept form (y=mx+b).

Slope-Intercept Form

Use y=mx+b directly.

Find the slope just like the above, so m=\frac{3}{2}.

Now, plug one of the points (either one!) together with <em>m</em> into

y=mx+b\\-2=\frac{3}{2}(2)+b \\ -2=3+b \\ b=-5

Now you know the value of <em>b</em>, so the equation for the line is

y=\frac{3}{2}x-5

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