Explanation:
To find the equation of a line that is perpendicular to y = -x + 4, we need to determine its slope first.
The given equation is in slope-intercept form y = mx + b, where m is the slope of the line. In this case, the slope is -1, since the coefficient of x is -1.
The slope of any line perpendicular to this line would be the negative reciprocal of the slope of the given line. That is, if m1 is the slope of the given line, then the slope of the perpendicular line would be m2 = -1/m1.
Therefore, the slope of the line perpendicular to y = -x + 4 is m2 = -1/(-1) = 1.
Now, we have the slope (m = 1) and a point (-2, 10) that the line passes through. We can use the point-slope form of the equation of a line to find its equation:
y - y1 = m(x - x1)
where (x1, y1) is the given point, and m is the slope.
Plugging in the values, we get:
y - 10 = 1(x - (-2))
y - 10 = x + 2
y = x + 12
Therefore, the equation of the line that is perpendicular to y = -x + 4 and passes through the point (-2, 10) is y = x + 12 in slope-intercept form.