Question

IWhat is the equation of a line that passes through the points (3, 6) and (8, 4)?

Answer 1

`(x_1 =2, y_1 = 6), (x_2 = 2, y_2 = 4)`

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

And replacing we got:

`m=(4-6)/(8-3)= -(2)/(5)`

And for this case we can use the first point to find the intercept like this:

`6 = -(2)/(5)(3) +b`

And solving we got:

`b = 6 +(6)/(5)= (36)/(5)`

And then the line equation would be given by:

`y = -(2)/(5)x +(36)/(5)`

Explanation:

For this case we have the following two points given:

`(x_1 =2, y_1 = 6), (x_2 = 2, y_2 = 4)`

And for this case we want an equation for a line with the two points given by:

`y = mx+b`

Wher m is the slope and b the y intercept. We can find the slope with this formula:

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

And replacing we got:

`m=(4-6)/(8-3)= -(2)/(5)`

And for this case we can use the first point to find the intercept like this:

`6 = -(2)/(5)(3) +b`

And solving we got:

`b = 6 +(6)/(5)= (36)/(5)`

And then the line equation would be given by:

`y = -(2)/(5)x +(36)/(5)`