To find the y-intercept of the line given by the equation x + 5y = 12, we first need to express the equation in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
We can start by isolating y. First, we can rearrange the equation:
5y = 12 – x
Next, divide each term by 5 to solve for y:
y = - rac{1}{5}x + rac{12}{5}
Now, we can see that the equation is in slope-intercept form. The y-intercept b is the value of y when x = 0.
From our equation, when x = 0, y = rac{12}{5}. Therefore, the y-intercept of the line is:
b = rac{12}{5}
Thus, the y-intercept of the line is rac{12}{5} or 2.4.