Question

Instructions: Find the equation of the line through point (5,4)

and perpendicular to y=−43x−2
. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12
).

Answer 1

The equation of the line is,

y = 3/4x + 1/4

Explanation:

We use the general slope-intercept form of linear equation and solve for m and b to find the required line

y = mx + b

Since the required line passes through (5, 4),

Our general equation satisfies,

4 = m(5) + b (i)

Now, it is perpendicular to y = -4/3x - 2

here, -4/3 is the slope of this line and then for the required line we observe that,

Since the slopes of perpendicular lines are negative reciprocals of each other, we have,

m = -1/(-4/3)

m = 3/4

Putting this into (i),

4 = (3/4)(5) + b

b = 4 - 15/4

b = 1/4

And we get the required line,

y = 3/4x + 1/4