Final answer:
The equation of the line that goes through the point (2, 10) and is parallel to the line y = 2x + 12 is y = 2x + 6.
Step-by-step explanation:
To find the equation of a line that is parallel to another line, we need to know that parallel lines have the same slope. The original line has a slope of 2, so the parallel line will also have a slope of 2. We can use the point-slope form of a linear equation to find the equation of the parallel line: y - y₁ = m(x - x₁)
Using the point (2, 10) and the slope m = 2, we can substitute the values into the equation: y - 10 = 2(x - 2)
Simplifying the equation gives us: y - 10 = 2x - 4
Finally, rearranging the equation to slope-intercept form gives us the answer: y = 2x + 6