6. what is an equation of the line that passes through the point (-2,1) and is parallel to the line x - 2y =…
6. what is an equation of the line that passes through the point (-2,1) and is parallel to the line x - 2y = 2?
Answer
Explanation:
Step1: Find the slope of the given line.
Rewrite $x - 2y=2$ in slope - intercept form $y = mx + b$ (where $m$ is the slope). $-2y=-x + 2$, so $y=\frac{1}{2}x - 1$. The slope $m=\frac{1}{2}$.
Step2: Use the point - slope form of a line.
The point - slope form is $y - y_1=m(x - x_1)$, with $(x_1,y_1)=(-2,1)$ and $m = \frac{1}{2}$. $y - 1=\frac{1}{2}(x+2)$
Step3: Simplify the equation.
$y - 1=\frac{1}{2}x + 1$ $y=\frac{1}{2}x+2$ or $x - 2y=-4$
Answer:
$y=\frac{1}{2}x + 2$ (or $x - 2y=-4$)