Question

What is the equation in standard form has a graph that passes through the point (5,-3) and has a slope of 6/5. Can 6x - 5y=45 be?

Answer 1

6x - 5y = 45

Explanation:

Firstly obtain the equation in slope- intercept form

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

given slope m =
`(6)/(5)` , then

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

to find c , substitute the point (5, - 3 ) into the partial equation

- 3 =
`(6)/(5)` (5) + c = 6 + c ( subtract 6 from both sides )

- 9 = c

y =
`(6)/(5)` x - 9 ← equation in slope- intercept form

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

from the equation in slope- intercept form

y =
`(6)/(5)` x - 9 ( multiply through by 5 to clear the fraction )

5y = 6x - 45 ( add 45 to both sides )

45 + 5y = 6x ( subtract 5y from both sides )

45 = 6x - 5y , that is

6x - 5y = 45 ← in standard form