what is an equation of the line that passes through the point (2,5) and is parallel to the line x - 2y = 6?

Explanation:

Step1: Find the slope of the given line

Rewrite $x - 2y=6$ in slope - intercept form $y = mx + b$ ($m$ is slope, $b$ is y - intercept). $x-2y = 6$ can be rewritten as $y=\frac{1}{2}x - 3$, so the slope $m=\frac{1}{2}$. Since parallel lines have the same slope, the slope of the required line is also $\frac{1}{2}$.

Step2: Use the point - slope form to find the equation of the line

The point - slope form is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(2,5)$ and $m = \frac{1}{2}$. Substitute the values: $y - 5=\frac{1}{2}(x - 2)$.

Step3: Simplify the equation

Expand the right - hand side: $y - 5=\frac{1}{2}x-1$. Add 5 to both sides to get the slope - intercept form: $y=\frac{1}{2}x + 4$. We can also write it in general form: $x-2y=-8$.

Answer:

$y=\frac{1}{2}x + 4$ (or $x - 2y=-8$)