Final answer:
To find the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
Step-by-step explanation:
To find the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. First, let's find the slope of the given line x + y = -5 by putting it in slope-intercept form (y = mx + b).
Subtract x from both sides: y = -x - 5. Now we can see that the slope of this line is -1.
The negative reciprocal of -1 is 1. So, the slope of the line perpendicular to x + y = -5 is 1. Using the point-slope form (y - y1 = m(x - x1)), we can now write the equation of the line that passes through the point (7, 3):
y - 3 = 1(x - 7)
y - 3 = x - 7
y = x - 4
Therefore, the equation of the line that is perpendicular to x + y = -5 and passes through the point (7, 3) is y = x - 4.