Question

Write the equation of the line in slope-intercept form that passes through the given points: (0,5) and (3, 0)​

Answer 1

Given :-

• Two points (0,5) and (3,0)

To find:-

• The equation of the line passing through the given points.

Answer :-

We are here given two points (0,5) and (3,0) and we are interested in finding the equation of the passing through the given points. Firstly let's find out the slope as ,

`\implies m =(y_2-y_1)/(x_2-x_1)\\`

and here ,

• 
  `x_1 = 0`
• 
  `x_2 = 3`
• 
  `y_1= 5`
• 
  `y_2 = 0`

substitute the respective values in the formula of slope stated above as ,

`\implies m =( 0-5)/(3-0) \\`

`\implies\underline{\underline{ m = (-5)/(3)}} \\`

Now we can use the point slope form of the line to find out the equation of the given line . The point slope form of the line is ,

`\implies y - y_1 = m(x - x_1) \dots(i) \\`

Slope intercept form of the line is
`y = mx + c` , where
`m` is the slope of the line and
`c` is y intercept.

Take any point out of the given two , say (3,0) . So here,

• 
  `x_1 = 3`
• 
  `y_1 = 0`
• 
  `m =(-5)/(3)`

substitute the respective values in (i) as ,

`\implies y -0 = (-5)/(3)( x -3)\\`

`\implies y = (-5)/(3)x + (-5)/(3)* -3 \\`

`\implies \underline{\underline{ y =(-5)/(3)x + 5}} \\`

This is our required equation in the slope intercept form.

And we are done!