Question

How do you find a standard form equation for the line with (-3,6) and slope 7/8?

Answer 1

see a solution process below;

Explanation:

Recall, the standard form for the equation of a line is;

`y = mx + c`

Where;

`x and y = "coordinates"`

`m = "slope"`

`c = "intercept"`

`y = mx + c - - - eqn**`

`x = -3`

`y = 6`

`m = 7/8`

Substituting the parameters into `eqn**`

`6 = 7/8(-3) + c`

`6 = -21/8 + c`

Multiplying through by `8`

`8(6) = 8(-21/8) + 8(c)`

`48 = cancel8(-21/cancel8) + 8c`

`48 = -21 + 8c`

Collect like terms..

`48 + 21 = 8c`

`69 = 8c`

`c = 69/8`

Substituting the value of `c` into the main equation;

`y = mx + 69/8`

Multiply through by `8`

`8(y) = 8mx + 8(69/8)`

`8y = 8mx + cancel8(69/cancel8)`

`8y = 8mx + 69`

Recall; `m = 7/8`

`8y = 8(7/8)x + 69`

`8y = cancel8(7/cancel8)x + 69`

`8y = 7x + 69 -> "equation"`

Hope this helps!