Question

What are the coordinates of the y-intercept of the line who's equation is 12x + 13y =8???

Answer 1

y-intercept = (0,
`(8)/(13)` ).

Explanation:

Given the linear equation in standard form, 12x + 13y = 8:

We must transform this equation into slope-intercept form to make it easier to determine the coordinates of the y-intercept.

12x + 13y = 8

Subtract 12x from both sides:

12x + 13y - 12x = - 12x + 8

13y = - 12x + 8

Next, divide both sides of the equation by 13 to solve for y:

`(13y)/(13) = (-12x + 8)/(13)`

`y = (-12x + 8)/(13)` or
`y = -(12)/(13) x + (8)/(13)`

Next, to determine the y-intercept, we must set x = 0 (because the y-intercept is the point where the graph of the linear equation crosses the y-axis).

Let x = 0:

`y = -(12)/(13) x + (8)/(13)`

`y = -(12)/(13) (0) + (8)/(13)`

`y = (8)/(13)`

Therefore, the value of y when x = 0 is
`(8)/(13)` . This is the y-intercept, and its coordinate is (0,
`(8)/(13)` ).