Question

Find the equation of the line that passes through negative 3 and negative 3 and that is parallel to X - to Y equals negative 7

Answer 1

The given equation is

`x-2y=-7`

First, we find the slope of the given equation.

`\begin{gathered} -2y=-7-x \\ y=(-7-x)/(-2) \\ y=(7)/(2)+(x)/(2) \end{gathered}`

Remember that the slope is the coefficient of x. So, the slope of the given line is 1/2.

Since the new line must be parallel, then its slope is also 1/2.

According to the problem, the new line passes through (-3, -3). Let's use the point-slope formula to find the equation.

`\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=(1)/(2)(x-(-3)) \\ y+3=(1)/(2)x+(3)/(2) \\ y=(1)/(2)x+(3)/(2)-3 \\ y=(1)/(2)x-(3)/(2) \end{gathered}`

Therefore, the equation of the new parallel line is

`y=(1)/(2)x-(3)/(2)`