Question

Write the equation of a line parallel to the line
2x + 3y = 5 and passes through the point (9, -3)

Answer 1

Since, parallel lines have same slope
therefore,
Slope of required line = slope of 2x + 3y = 5
i.e. 3y= -2x+5
i.e. \[\huge y= \frac{-2}{3} x + 5 \]
Comparing the above equation with \[\huge y= m x +c\]
We find slope m= \[\huge m=\frac{-2}{3} \]
Silnce line passes through the point (9, -3)
Hence, eq of line in slope- point form is given as;
\[\huge y-y_1= m(x-x_1)\]
Where x1 = 9 & y1= -3
substituting the values of m, x1 & y1 in the above equation we find:
\[\huge y-(-3)= \frac{-2}{3}(x-9)\]
\[\huge y+3= \frac{-2}{3}(x-9) \rightarrow \huge 3( y+3)= -2(x-9)\]
\[\rightarrow \huge 3y+9= -2x+18\]
\[\rightarrow \huge 2x+3y=18+9\]
\[ \huge \rightarrow 2x+3y=27\]
hence \[ \huge 2x+3y=27 \] is the required equation of the line.
@purexyz

Answer 2

@purexyz

Answer 3

thanks