Question

Write the equation of the line that is parallel to the line 2x + 3y = 5 and contains the point (-2,1). O A 2x + 3y = -1 O B. 3x + 2y = 5 O c. 3x-2y=7 O D. 2x - 3y=7

Answer 1

Step 1

The equation of a line is given as

$\begin{gathered} y=mx+c \\ \text{where } \\ m\text{ = slope} \\ c\text{ = y-intercept} \end{gathered}$

The given equation is

$\begin{gathered} 2x+3y\text{ = 5} \\ 3y=5-2x \\ y=\frac{5}{3}-\frac{2x}{3} \\ m=-\frac{2}{3} \end{gathered}$

Step 2

For parallel lines their slopes are equal

$\text{Hence the slope of the line parallel to the given equation = -}\frac{2}{3}$

The equation of the required parallel line now becomes

$y=c-\frac{2}{3}x$

Step 3

Find the y-intercept

$\begin{gathered} \text{The given points are ( -2,1) in the form of (x,y)} \\ \text{Hence,} \\ 1=c-\frac{2}{3}(-2) \\ 1-\frac{4}{3}=c \\ c=-\frac{1}{3} \end{gathered}$

Step 4

Write the required equation

$\begin{gathered} y=-\frac{1}{3}-\frac{2}{3}x \\ 3y=-1-2x \\ 2x+3y=-1 \end{gathered}$

The answer is 2x+3y = -1