Question

Line CD passes through points C(3, -5) And D(6, 0). What is the equation of line CD in standard form?

Answer 1

Y = mx + b
m = (0 - -5)/(6 - 3) = 5/3
y = 5/3x + b
0 = 5/3(6) + b
b = -10
(y = 5/3x - 10)3
3y = 5x - 30
3y - 5x = -30
5x - 3y = 30

Answer 2

Answer:

5x - 3y = 30

Step-by-step explanation:

First we find the slope of the line using the formula

$m=\frac{y_2-y_1}{x_2-x_1}$

Using our points, we have

m = (-5-0)/(3-6) = -5/(-3) = 5/3

Next we write the equation using point-slope form.  Using the slope of 5/3 and the second point, we have

y-0 = 5/3(x-6)

y = 5/3(x-6)

Using the distributive property, we have

y = 5/3(x)-5/3(6)

y = 5/3(x)-5/3(6/1)

y = 5/3(x)-30/3

y = 5/3x - 10

We cannot have fractions in standard form.  To deal with this, we will multiply all 3 terms by 3:

3y = 5/3x(3) - 10(3)

3y = 5x - 30

We want x and y on the same side; subtract 5x from each side:

3y-5x = 5x-30-5x

-5x+3y = -30

We want x to be positive; multiply all 3 terms by -1:

5x-3y = 30