Final answer:
To find a line perpendicular to the given line y = -2x - 7, we need to find the negative reciprocal of the slope of the given line. We can then use the point-slope form of a linear equation to find the equation of the perpendicular line through the given point (-3, 10).
Step-by-step explanation:
To find a line perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line. In this case, the given line has a slope of -2.
The negative reciprocal of -2 is 1/2. So, the line perpendicular to y = -2x - 7 will have a slope of 1/2.
Next, we can use the point-slope form of a linear equation to find the equation of the perpendicular line.
The point-slope form is given by y - y1 = m(x - x1) where (x1, y1) is a point on the line and m is the slope.
Substituting the given point (-3, 10) and the slope 1/2 into the point-slope form, we get y - 10 = 1/2(x - (-3)).
Simplifying the equation, we get y - 10 = 1/2(x + 3).
This is the equation of the line perpendicular to y = -2x - 7 that passes through (-3, 10).