Question

Find the equation of the line through point (10,4) and parallel to 3x+5y=8. Use a slash ("/") for fractions (e.g. 1/2 for 12). DO not include spaces in your answers.

Answer 1

3x + 5y = 50

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3x + 5y = 8 ( subtract 3x from both sides )

5y = - 3x + 8 ( divide terms by 5 )

y = -
`(3)/(5)` x +
`(8)/(5)` ← in slope- intercept form

with slope m = -
`(3)/(5)`

Parallel lines have equal slopes , then

y = -
`(3)/(5)` x + c ← is the partial equation

to fid c substitute (10, 4 ) into the partial equation

4 = - 6 + c ⇒ c = 4 + 6 = 10

y = -
`(3)/(5)` x + 10 ← equation of parallel line in slope- intercept form

multiply through by 5 to clear the fraction

5y = - 3x + 50 ( add 3x to both sides )

3x + 5y = 50 ← equation of parallel line in standard form

Answer 2

Step-1: Convert the equation of the line into slope intercept form.

• 3x + 5y = 8
• => 5y = -3x + 8
• => y = -3x/5 + 8/5

In this case, the slope we obtained is -3/5, which is -0.6. Let's use point slope form to find the original equation.

Step-2: Use point slope form.

• y - y₁ = m(x - x₁)
• => y - 4 = -0.6(x - 10)
• => y - 4 = -0.6x + 6
• => y = -0.6x + 10