Equation of a line perpendicular to LM: y = 5x + 4, and passing through the point (-3, 2) is y = (-1/5)x + (7/5).
What is the equation of a line?
The equation of a line is the representation of a line on a coordinate (x and y) plane, which shows the relation between x and y, for every point on the particular line.
The standard form of a line is ax + by = c, where x and y are variables and a, b, and c are constants.
The slope-intercept form of a line is y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept of the line.
How are slopes of perpendicular lines related?
If the slope of two perpendicular lines is m1 and m2, then
m1*m2 = -1.
How do we solve the given question?
We are asked to find the equation of a line, which is perpendicular to the line LM: y = 5x + 4, and passes through the point (-3, 2).
Line LM is given in the slope-intercept form with slope m1 = 5, and y-intercept b1 = 4.
Let the line perpendicular to LM be AB, its slope be m2, and its y-intercept be b2.
As we know, the product of slopes of perpendicular lines = -1,
We take, m1*m2 = - 1, or, 5*m2 = -1, or, m2 = -1/5.
Therefore, the slope of line AB = -1/5.
To find its y-intercept b2, we substitute all values in the equation of a line in slope-intercept form with x = 2, and y = - 3, as AB passes through (-3, 2).
∴ 2 = (-1/5)(-3) + b2
or, b2 = 2 - 3/5 = 7/5.
Now we can find the equation of AB, using m = m2 = (-1/5) and b = b2 = (7/5).
∴ Equation of AB is: y = (-1/5)x + (7/5)
∴ Equation of a line perpendicular to LM: y = 5x + 4, and passing through the point (-3, 2) is y = (-1/5)x + (7/5).
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