Write the standard form of the equation of the line that pas

Write the standard form of the equation of the line that passes through the point (4,1)and is parallel to the line 3x + 2y = 5.

Solution

The desired equation can be worked out using the following general formula:

y - y1 = m( x -x1) where m is the slope and (x1,y1) is the one point we know - here (4,1)

To get the slope we rearrange the given line as y = -(3/2) x + 5/2 Once in this form we
see that the slope is -(3/2). Since we want a parallel line the slope m also equals -(3/2)
Putting this together we ge
y - 1 = -(3/2) ( x - 4)

This can be rearranged into the slope intercept form.
y = -(3/2) x + 7