Question

determine the equation of the line that passes through the following points (-2 1/4, 1 3/4) and (-3, 3)​

Answer 1

Answer:

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

Step-by-step explanation:

step 1

Convert mixed number to an improper fraction

$-2\frac{1}{4} =-2-\frac{1}{4}=-\frac{9}{4}$

$1\frac{3}{4} =1+\frac{3}{4}=\frac{7}{4}$

so

we have the points

$(-\frac{9}{4},\frac{7}{4})$ and $(-3,3)$

step 2

Find the slope of the line

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the points

$(-\frac{9}{4},\frac{7}{4})$ and $(-3,3)$

substitute

$m=\frac{3-(7/4)}{-3+(9/4)}$

$m=\frac{5/4}{-3/4}$

$m=-\frac{5}{3}$

step 3

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=-\frac{5}{3}$

$point\ (-3,3)$

substitute

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

step 4

Convert to slope intercept form

Isolate the variable y

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

$y=-\frac{5}{3}x-5+3$

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