Question

What is the slope of the line passing through these two points? ( 2, 5 ) and ( 3, 3) . Write this line in point-slope form.

Answer 1

We have;

• (x1=2,y1=5) & (x2=3,y2=3)

Now, By slope formula,

`\sf \large \: m = ( y _(2) - y_(1) )/( x_(2) - x_(1) )`

Putting the values,

`\sf \: m = (3 - 5)/(3 - 2)`

`\sf \: m = ( - 2)/(1) \: \:i.e \: \: m = - 2`

Let us now find the equation in slope intercept or point slope form

`\sf(y - y_(1) ) = m(x - x_(1))`

• x1 = 2 and y1 = 5

`\sf(y - 5) = - 2(x - 2)`

`\sf \: y - 5= - 2x + 4`

`\sf \: y = - 2x + 4 - 5`

`\boxed{\sf \: y = - 2x - 1}`