Question

Write the equation of a line that is parallel to y=1/2x-4 and that passes through the point (9 -6)

Answer 1

Equation of a line that is parallel to y=1/2x-4 and that passes through the point (9 -6) is 2y - x + 21 =0

Explanation:

Equation of line 1 is y=1/2x-4

Comparing it with form : y = m x + C, we get m = 1/2

So, the slope of line 1 = 1/2

Now, line 2 is parallel to line 1.

Slope of line 2 = slope of Line 1

⇒ Slope of line 2 = 1/2

The point (x0,y0) on the line 2 = (9,-6)

Now, by POINT SLOPE FORMULA:

The equation of a line with point (x0,y0) and slope m is given as

(y-y0)= m (x -x0)

So, here the equation of line 2 is:

`y - (-6) = (1)/(2)( x -9)\\\implies 2( y + 6 ) = x -9\\or, 2y - x  + 21 =0`

Hence, the equation of a line that is parallel to y=1/2x-4 and that passes through the point (9 -6) is 2y - x + 21 =0.