Final answer:
The equation of the line perpendicular to y = -4x - 6 that passes through (4,10) is y = 1/4x + 9. This was found using the negative reciprocal of the original slope and the point-slope form of a linear equation.
Step-by-step explanation:
To find the equation of a line that is perpendicular to y = -4x - 6 and passes through the point (4,10), first determine the slope of the given line. The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. In this case, the original slope is -4, so the slope of the perpendicular line is 1/4.
Using the point-slope form y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we plug in the slope of 1/4 and the point (4,10) to obtain the equation of the perpendicular line.
Substituting the values, we get the equation y - 10 = 1/4(x - 4). Simplifying this, we get:
- y - 10 = 1/4x - 1
- y = 1/4x + 9
Therefore, the equation of the line perpendicular to y = -4x - 6 that passes through the point (4,10) is y = 1/4x + 9.