Answer:
y = 1/43x + 167/43.
Explanation:
y = -43x - 2 is in the slope-intercept form of a line, whose general equation is given by:
y = mx + b, where
- (x, y) is any point on the line,
- m is the slope,
- and b is the y-intercept.
Thus, we want the equation of the other line to also be in slope-intercept form.
The slopes of perpendicular lines are negative reciprocals of each other as shown by the formula;
m2 = -1/m1, where
- m2 is the slope of the line we're trying to find,
- and m1 is the slope of the line we know.
Finding m2:
Thus, we can find m2, the slope of the other line, by plugging in -43 for m1:
m2 = -1/-43
m2 = 1/43
Thus, the slope of the other line is 1/43
Finding b:
We can find b, the y-intercept of the other line by plugging in (5, 4) for (x, y) and 1/43 for m in the slope-intercept form:
4 = 1/43(5) + b
(4 = 5/43 + b) - 5/43
167/43 = b
Thus, the y-intercept of the other line is 167/43.
Therefore, the equation of the line through the point (5, 4) and perpendicular to y = -43x - 2 is y = 1/43x + 167/43.