SOLUTION: i have a problem that says solve for k where the equation is 4x-ky-7=0 and the slope is = to 3. How do I solve for k?

Question 271277: i have a problem that says solve for k where the equation is 4x-ky-7=0 and the slope is = to 3. How do I solve for k?
Found 2 solutions by CharlesG2, jsmallt9:
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
i have a problem that says solve for k where the equation is 4x-ky-7=0 and the slope is = to 3. How do I solve for k?
4x-ky-7=0 (the equation of a line is y=mx+b where m is the slope and b is the y-intercept (or vertical intercept or point (0,b)))
-ky = -4x + 7
ky = 4x - 7
y = 4/k * x - 7/k
said the slope = 3, so m=3 and m=4/k and 4/k = 3
4/k = 3 (multiply both sides by k)
4 = 3k
4/3 = k
b= -7/k = -7/(4/3)
(4/3)b = -7
4b = -21
b = -21/4
y = 3x - 21/4

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
There are a couple of ways to solve this problem:
First, this equation is (or is nearly) in standard form. And there is a formula for the slope of an equation in standard form: . Since the slope, m, is 3 and A = 4 and B = -k, this formula for this equation is

We can solve this for k. Multiply both sides by k:

Divide both sides by 3:

Solve for y first. (You'll see why when we get there.

I'll start by adding ky to each side:

Instead of dividing by k I am going to multiply both sides by 1/k. Multiplying by the reciprocal of k is equivalent to dividing by k. But it leaves the equation in a much better form:

Using the Distributive property on the left side we get:

We have solved the equation for y. This puts the equation in Slope-intercept form. The slope is coefficient of x: 4/k. The slope is supposed to be 3 so:

Solving this for k we get:

The first way was easier but it requires that you know the slope formula for equations of lines in Standard Form.
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