Question

Line m in xy plane contains the points (2,4) and (0,1) which of the following is the equation of M

Answer 1

Answer:

The equation of line M in slope intercept form is    $y=\frac{3}{2}x+1$

The equation of line M in standard form is  $3x-2y=-2$

Step-by-step explanation:

step 1

Find the slope of line M

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

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

we have the points

(2,4) and (0,1)

substitute

$m=\frac{1-4}{0-2}$

$m=\frac{-3}{-2}$

$m=\frac{3}{2}$

step 2

Find the equation of the line M in point slope form

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

we have

$m=\frac{3}{2}$

$point\ (0,1)$

substitute

$y-1=\frac{3}{2}(x-0)$

$y-1=\frac{3}{2}x$ ----> equation in point slope form

step 3

Find the equation of line M in slope intercept form

$y=mx+b$

Isolate the variable y in the equation of the line in point slope form

$y-1=\frac{3}{2}x$

Adds 1 both sides

$y=\frac{3}{2}x+1$

step 4

Find the equation of the line M in standard form

$Ax+By=C$

where

A is a positive integer

B and C are integers

we have

$y=\frac{3}{2}x+1$

Multiply by 2 both sides

$2y=3x+2$

$3x-2y=-2$ ---> equation in standard form