Final answer:
To find the equation of a line perpendicular to another line, determine the slope of the original line and take its negative reciprocal. Using the point-slope form of a line and the given point, substitute the values to find the equation.
Step-by-step explanation:
To find the equation of a line perpendicular to another line, we first need to determine the slope of the original line. The given equation of the line is 4x + y = 7. We can rewrite it in slope-intercept form as y = -4x + 7. The slope of the original line is -4. The slope of a line perpendicular to it is the negative reciprocal of -4, which is 1/4. Using the point (-4, -3) and the slope 1/4, we can use the point-slope form of a line to find the equation of the perpendicular line:
y - y1 = m(x - x1)
Substituting (-4, -3) for (x1, y1) and 1/4 for m, we get:
y - (-3) = 1/4(x - (-4))
Simplifying the equation, we have:
y + 3 = 1/4(x + 4)
This is the equation of the line passing through (-4, -3) and perpendicular to 4x + y = 7.