Final answer:
The y-intercept in the linear equation y=32x-4 is the constant term, which is -4. This means the line crosses the y-axis at the point (0, -4). The y-intercept is an important concept as it helps describe the position of the line on a graph.
Step-by-step explanation:
The y-intercept in the linear equation y=32x−4 is a key feature of the equation. When looking at the standard form of a linear equation, which is y = mx + b, the y-intercept is represented by the 'b' term. This is the value of y at the point where the line crosses the y-axis. To find the y-intercept, simply look for the constant term in the equation without any x attached to it.
In our specific equation, y=32x−4, the constant term is −4. Therefore, the y-intercept is −4. This indicates that the line crosses the y-axis at the point (0, -4). No further calculation is needed as the y-intercept is explicitly given in the equation. If you were to graph this line, you would start at the point (0, -4) on the y-axis and use the slope, which is 32 in this case, to determine the angle of the line's ascent from the y-intercept.
The concept of the y-intercept is fundamental in algebra and helps to provide a complete picture of a line's graph on a two-dimensional plane. It is especially important in various applications of mathematics, including data analysis and predictions based on linear models.