Question

How do you write the equation of the line that passes through the points (2,5) and (6,2)?

Answer 1

The equation of line in slope-intercept form is `y = -3/4 x +6 1/2`
The equation of line in standard form is `3x + 4y = 26`

Explanation:

The slope of the line passing through `(2,5) and (6,2)` is `m= (y_2-y_1)/(x_2-x_1)= (2-5)/(6-2)=-3/4`

Let the equation of the line in slope-intercept form be `y=mx+c or y=-3/4x+c` The point (2,5) will satisfy the equation . So, `5= -3/4*2+c or c= 5+3/2= 13/2`

Hence the equation of the line in slope-intercept form is `y= -3/4x+13/2 or y = -3/4 x +6 1/2`

The equation of the line in standard form is `y= -3/4 x+13/2. or 4y =-3x+26 or 3x + 4y = 26` [Ans]