inal answer:
The equation of the line that is perpendicular to y=-2x+6 and passes through the point (4, 2) is y = 1/2x + 2. To find it, calculate the negative reciprocal of the original slope, then use the point-slope formula and simplify into slope-intercept form.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another and passes through a given point, we first need to understand the relationship between the slopes of perpendicular lines. If the slope of one line is m, the slope of a line perpendicular to it will be -1/m. The given line has an equation y = -2x + 6, so its slope is -2. Therefore, the slope of the perpendicular line will be 1/2 (since -1/(-2) = 1/2).
Now that we have the slope, we can use the point-slope form of a line to find our equation. The point given is (4, 2), so we plug the slope and this point into the point-slope formula y - y1 = m(x - x1), resulting in y - 2 = 1/2(x - 4). Simplifying, we get y - 2 = 1/2x - 2, and then adding 2 to both sides gives us the slope-intercept form of the line: y = 1/2x + 2.