Final answer:
The standard form of the equation of a line is Ax + By = C. By using the point-slope form and rearranging the equation, we can find the standard form. The examples given provide step-by-step solutions for finding the standard form of the equations.
Step-by-step explanation:
The standard form of the equation of a line is given by:
Ax + By = C
where A, B, and C are constants.
To find the standard form of the equation of a line, we can use the point-slope form and rearrange the equation.
Let's solve the examples:
1. Through: (3, -1), slope = -1
Using the point-slope form, we have:
y - y1 = m(x - x1)
Substituting the values, we get:
y - (-1) = -1(x - 3)
Simplifying, we have:
y + 1 = -x + 3
Rearranging the equation, we get:
x + y = 2
So, the standard form of the equation is x + y = 2.
2. Through: (-2, 5), slope = -4
Using the point-slope form, we have:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 5 = -4(x - (-2))
Simplifying, we have:
y - 5 = -4(x + 2)
Rearranging the equation, we get:
4x + y = -13
So, the standard form of the equation is 4x + y = -13.
3. Through: (3, 5), slope = 5/3
Using the point-slope form, we have:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 5 = (5/3)(x - 3)
Simplifying, we have:
y - 5 = (5/3)x - 5
Rearranging the equation, we get:
(5/3)x + y = 0
Multiplying all terms by 3 to eliminate the fraction, we get:
5x + 3y = 0
So, the standard form of the equation is 5x + 3y = 0.