Question

Write an equation in standard form for a line that passes through point (-3,5) and has a slope of 3/4

pls help!!

Answer 1

3x - 4y = - 29

Explanation:

the equation of a line in standard form is

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

We can first obtain the equation in slope- intercept form

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

given slope m =
`(3)/(4)` , then

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

to find c, substitute the point (- 3, 5 ) for x and y into the partial equation

5 =
`(3)/(4)` (- 3) + c = -
`(9)/(4)` + c ( add
`(9)/(4)` to both sides )

`(20)/(4)` +
`(9)/(4)` = c , then

c =
`(29)/(4)`

y =
`(3)/(4)` x +
`(29)/(4)` ← in slope- intercept form

multiply through by 4 to clear the fractions

4y = 3x + 29 ( subtract 3x from both sides )

- 3x + 4y = 29 ( multiply through by - 1 )

3x - 4y = - 29 ← equation in standard form