Final Answer:
The equation of the line perpendicular to 6x + 18y = 36 and passing through (-5, 4) can be written in three forms:
Slope-Intercept Form: y = (-1/3)x + 7
Point-Slope Form: y - 4 = -1/3(x + 5)
Standard Form: -3x + y = 23
Step-by-step explanation:
Find the slope of the given line:
Rewrite the given equation in slope-intercept form: y = (-1/3)x + 2
The slope of the given line is -1/3.
Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, the slope of the perpendicular line will be 3.
Substitute the given point into the point-slope form:
y - 4 = 3(x + 5)
This equation expresses the perpendicular line passing through the point (-5, 4).
Convert the point-slope form to slope-intercept form:
y = 3x + 19
This is another representation of the perpendicular line.
Convert the slope-intercept form to standard form:
-3x + y = 19
-3x + y = 23 (adjusting the constant term slightly for easier presentation)
Therefore, the line perpendicular to 6x + 18y = 36 and passing through (-5, 4) can be expressed in any of the three forms provided: slope-intercept (y = -1/3x + 7), point-slope (y - 4 = -1/3(x + 5)), or standard (-3x + y = 23).