Explanation:
To convert the equation y - 4 = (3/5)(x - 10) into standard form, you'll need to eliminate the fractions and rearrange the variables to have the equation in the form of Ax + By = C, where A, B, and C are integers.
Let's start by distributing the (3/5) to the terms inside the parentheses:
y - 4 = (3/5)(x - 10)
y - 4 = (3/5)x - (3/5) * 10
y - 4 = (3/5)x - 6
Next, let's get rid of the fraction by multiplying both sides of the equation by 5 to clear the denominators:
5(y - 4) = 5[(3/5)x - 6]
5y - 20 = 3x - 30
Now, let's rearrange the equation to have the x and y terms on the left side and the constant term on the right side:
3x - 5y = -20 + 30
3x - 5y = 10
So, the standard form of the equation is 3x - 5y = 10.