Question

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 slope of given line

Rewrite \(x - 2y = 6\) in slope - intercept form \(y=mx + b\) (where \(m\) is slope).
Subtract \(x\) from both sides: \(-2y=-x + 6\).
Divide by \(-2\): \(y=\frac{1}{2}x-3\). So slope \(m = \frac{1}{2}\).

Step2: Use point - slope form for parallel line

Parallel lines have equal slopes, so new line has \(m=\frac{1}{2}\) and passes through \((2,5)\).
Point - slope formula: \(y - y_1=m(x - x_1)\) (where \((x_1,y_1)=(2,5)\)).
Substitute: \(y - 5=\frac{1}{2}(x - 2)\).

Step3: Simplify to slope - intercept form (optional, but common)

Distribute \(\frac{1}{2}\): \(y - 5=\frac{1}{2}x-1\).
Add 5 to both sides: \(y=\frac{1}{2}x + 4\).
(Or in standard form: \(x-2y=-8\), but slope - intercept is also correct.)

Answer:

The equation of the line is \(y=\frac{1}{2}x + 4\) (or equivalent forms like \(x - 2y=-8\) or \(y - 5=\frac{1}{2}(x - 2)\)).