Question

find an equation of the line through (2,6) and parallel to y = 2x + 5. y = (type your answer in slope - intercept form.)

Explanation:

Step1: Determine the slope

Parallel lines have equal slopes. The slope of the line $y = 2x+5$ is $m = 2$, so the slope of the required line is also $m = 2$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(2,6)$ and $m = 2$. Substitute these values: $y - 6=2(x - 2)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y-6 = 2x-4$. Then add 6 to both sides to get $y=2x + 2$.

Answer:

$y = 2x+2$