Question

Write an equation of the line that passes through the given point and is parallel to the given line.

Answer 1

Answer : Equation of line is y=Equation of line is y=$\frac{2}{3}$x+$\frac{-5}{3}$

Step-by-step explanation:

Theory :

Equation of line is given as y = mx + c.

Where, m is slope and c is y intercepted.

Slope of given line : y = $\frac{2}{3}$x+1 is m= $\frac{2}{3}$

We know that line : y = $\frac{2}{3}$x+1 is parallel to equation of target line.

therefore, slope of target line will be $\frac{2}{3}$.

we write equation of target line as y= $\frac{2}{3}$x+c

Now, It is given that target line passes through point ( -5,-2)

hence, point ( -5,-2) satisfy the target line's equation.

we get,

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

-2= $\frac{2}{3}$ $\times$ -5+ c

-5= $\frac{-10}{3}$+c

c= $\frac{-5}{3}$

thus, Equation of line is y=Equation of line is y=$\frac{2}{3}$x+$\frac{-5}{3}$