Answer:
y-intercept = (0, [tex]\frac{8}{13}[/tex] ).
Step-by-step 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:
[tex]\frac{13y}{13} = \frac{-12x + 8}{13}[/tex]
[tex]y = \frac{-12x + 8}{13}[/tex] or [tex]y = -\frac{12}{13} x + \frac{8}{13}[/tex]
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:
[tex]y = -\frac{12}{13} x + \frac{8}{13}[/tex]
[tex]y = -\frac{12}{13} (0) + \frac{8}{13}[/tex]
[tex]y = \frac{8}{13}[/tex]
Therefore, the value of y when x = 0 is [tex]\frac{8}{13}[/tex] . This is the y-intercept, and its coordinate is (0, [tex]\frac{8}{13}[/tex] ).
