Question

Write the standard form of the equation of the line through the given point with the given slope.

Through: (3, -1), slope = -1
Through: (-2, 5), slope = -4
Through: (3, 5), slope = 5/3

Answer 1

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.