Question

Write an equation of the line passing through each of the following pairs of points.

(0, 0), (4, 3)

Answer 1

y =
`(3)/(4)` x

Explanation:

The equation of a line passing through the origin (0, 0 ) is

y = mx ( where m is the slope )

m =
`(rise)/(run)` =
`(3)/(4)`, thus

y =
`(3)/(4)` x

Answer 2

The equation of the line passing through (0,0) and (4,3) is
`y=(3)/(4) x`

Solution:

Given pair of points are (0,0) and (4,3)

Here,
`x_(1)=0 ; y_(1)=0 ; x_(2)=4 ; y_(2)=3`

We know the slope of an equation is given by y = mx+c

Where “m” is the slope of the line and “c” is the y-intercept

To find the value of m, we use the below given formula

`\mathrm{m}=(y_(2)-y_(1))/(x_(2)-x_(1))`

Substituting the values we get,

`\mathrm{m}=(3-0)/(4-0)=(3)/(4)`

Putting the value of m in the slope intercept form we get,

`y=(3)/(4)x + c`

To find the value of c, we substitute the value of x and y from any two given point. Lets take x = 4 and y = 3

`\begin{array}{l}{3=(3)/(4)(4)+c} \\ {3=3+c} \\ {c=0}\end{array}`

Therefore the slope intercept equation becomes
`y=(3)/(4) x`