The equation that represents the canned goods order is 24x + 64y = 384, where x = number of minutes for producing fruit cans and y = number of minutes for producing vegetable cans.
What is the meaning of the y-intercept?
The y-intercept is the point where the line represented by the equation intersects the y-axis, which is when x = 0. In this case, when x = 0, the equation becomes 64y = 384, which simplifies to y = 6. Therefore, the y-intercept is 6, which represents the number of minutes it would take to produce only vegetable cans (with no fruit cans being produced).
In the equation 24x + 64y = 384, the y-intercept refers to the value of y when x is 0.
To find the y-intercept, we set x = 0 in the equation and solve for y:
24(0) + 64y = 384
64y = 384
y = 384/64
y = 6
Therefore, the y-intercept is 6. In the context of the equation, it means that if no fruit cans are produced (x=0), the number of minutes required to produce vegetable cans is 6.