Two lines passing through (3, 2) make an angle of 45°. If the slope of one of the lines is 11 find the slope of the other line.
1/3
one third
🙌
let the slope of the other be m
the angle between them is 45°, and we know that tan 45 = 1
(m - 11)/(1 + 11m) = 1
1 + 11m = m - 11
10m = -12
m = -1.2
To find the slope of the other line, we first need to find the slope of the line that passes through (3, 2) with a slope of 11.
The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope and b represents the y-intercept.
Since we know the slope (m = 11) and a point on the line (3, 2), we can substitute these values into the equation and solve for the y-intercept (b).
Using the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope, we have:
y - 2 = 11(x - 3).
Simplifying the equation, we get:
y - 2 = 11x - 33.
To isolate y, we add 2 to both sides:
y = 11x - 33 + 2.
y = 11x - 31.
Now that we have the equation of the line passing through (3, 2) with a slope of 11, we can determine the slope of the other line.
Since the two lines make an angle of 45°, they are perpendicular to each other. Perpendicular lines have negative reciprocal slopes. The negative reciprocal of 11 can be found by taking the negative inverse, which is -1/11.
Therefore, the slope of the other line is -1/11.