Question

What is the equation of the line with slope `m= -36/49` that passes through `(-6/7, 16/21)`?

Answer 1

`y=-36/49x+1432/1029` or

`y=-36/49x+1 403/1029`

Explanation:

`y-y_1=m(x-x_1)`

From the question, we get the following information:

`m=-36/49,`

`x_1,y_1=(-6/7,16/21)`

The point slope equation.

`y-16/21=-36/49(x-6/7)`

Simplify.

`y-16/21=-36/49x+216/343` `lArr` Multiplying two negatives gives a positive result.

Add `16/21` to both sides.

`y-color(red)cancel(color(black)(16/21))+color(red)cancel(color(black)(16/21))=-36/49x+216/343+16/21`

Simplify.

`y=-36/49x+216/343+16/21`

When adding fractions, the denominators must be the same. The Least Common Denominator (LCD) can be found by factoring the denominators.

Prime factorize the denominators `343` and `21`.

`343:` `7xx7xx7`

`21:` `3xx7`#

`"LCD"=3xx7xx7xx7=1029`

Multiply each fraction by the equivalent fraction that will result in the LCD `1029`. An equivalent fraction is equal to `1`, such as `2/2=1`.

`y=-36/49x-(216)/(343)xxcolor(red)(3/3)+16/21xxcolor(green)(49/49)`

Simplify.

`y=-36/49x+(648)/(1029)+(784)/(1029)`

Simplify.

`y=-36/49x+1432/1029` or

`y=-36/49x+1 403/1029`

Answer 2

`y = -36/49x + 136/1029`

Explanation:

Use the slope - intercept equation:`y = mx + b`

`y = -36/49 x + b`

Put the point `(-6/7, 16/21)` into the equation as `x " and " y`:

`16/21 = -36/49 * -6/7 + b`

`16/21 = 216/343 + b`

`b = 16/21 - 216/343`

Find a common denominator: `21 = 3 * 7; 343 = 7^3`

Common denominator `= 3 * 7^3 = 1029`

`b = 16/21 * 49/49 - 216/343 * 3/3 = 784/1029 - 648/1029 = 136/1029`

`y = -36/49 x + 136/1029`