Question

A line with a slope of -2/3 passes through the point (7,7). The equation of the line in standard form can be given by the formula Ax+By=C. Find A, B, and C.​

Answer 1

A = 2, B = 3, C = 35

Explanation:

the equation of a line in slope- intercept form is

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

here slope m = -
`(2)/(3)` , then

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

to find c substitute (7, 7 ) into the partial equation

7 = -
`(2)/(3)` (7) + c = -
`(14)/(3)` + c ( add
`(14)/(3)` to both sides )

7 +
`(14)/(3)` = c , then

c =
`(21)/(3)` +
`(14)/(3)` =
`(35)/(3)`

y = -
`(2)/(3)` x +
`(35)/(3)` ← equation in slope- intercept form

multiply through by 3 to clear the fractions

3y = - 2x + 35 ( add 2x to both sides )

2x + 3y = 35 ← equation in standard form

with A = 2 , B = 3 , C = 35