# Find the equation of the line that passes through the points (0,2) and (2,-3)

hala718 | Certified Educator

We have the point (0,2) and (2,-3) passes through a line.

Then we will use the slope form to determine the line.

The standard for is:

y-ya = m (x-x1)  such thatL

(x1,y1) is any point passes through the line

m is the slope such that:

m= (y2-y1)/x2-x1)

= (-3-2)/(2-0)

= -5/2

Then the slope m= -5/2

Then we will subsitute with the slope m= -5/2 and the point (0,2)

==> y-2 = (-5/2)(x-0)

==> y- 2 = (-5/2)x

Now add 2 to both sides:

==> y= (-5/2)x + 2

Multiply by 2:

==> 2y= -5x + 2

==> 2y + 5x + 2    is the equation for the line.

neela | Student

To find the equation of the line that passes through (0,2) and (2,-3).

We know that the equation the  line that passes through (x1,y1) and (x2, y2) is given by:

(y-y1) = {(y2-y1)/(x2-x1)} (x-x1).

We substitute (x1,y1) = (0,2) and (x2,y2) = (2,-3) in the formula , and we get:

y-2 = {(-3-2)/(2-0)} (x-0)

y-2 = (-5/2)x

2(y-2) = -5x.

2y-4 = -5x

5x+2y-4 = 0

Therefore 5x+2y -4 is the line that passes through (0,2) and (2, -3).
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