Through ( 3 , 4 ) and perpendicular to y = ( 1 / 3 ) x - 3

Answer 1

Another way to solve this problem is to use slope intercept form and solve for b (the Y intercept) by plugging in the X and Y values of the point that you know the line crosses (3,4).

The general formula of Slope Intercept Form is y = mx + b. M is the slope of the line, and b is where the line intercepts the Y axis. 

Given that we know the slope of the perpendicular line, we are able to figure out the slope of this line.

The slope's of perpendicular lines are negative reciprocals. In other words, when one line has a slope of m, a perpendicular line has a slope of −1/m.

This means that the slope will have the opposite sign of the perpendicular line, and the reciprocal of the slope of the perpendicular line. You can find the negative reciprocal by changing the sign (+ or -) and dividing 1 by the slope.

Examples:

1. the negative reciprocal of 2/3 is -3/2
2. the negative reciprocal of -5 is 1/5

Taking this in mind, we know that the slope of the perpendicular line is 1/3. That means that the slope of the line you're trying to find is -3.

Now that we know the slope, we can plug in the point that we know the line goes through (3,4) to the equation y = mx + b.

We know that m (the slope of the line) = -3, and we know that when X = 3, Y = 4.

So we get:

4 = -3*3 + b

Now we solve for b:

4 = -9 + b

13 = b

Now we can write the equation in slope intercept form:

y = -3x + 13

Answer 2

When two lines are perpendicular, their slopes are the negative reciprocal.

m = -3/1 = -3 with the given point: (3, 4)

y - y₀ = m(x - x₀)

y - 4 = -3(x - 3)

y - 4 = -3x + 9

y = -3x + 13 → 3x + y = 13