Final answer:
The y-intercept of the line y=8x–7 is -7, which is the point where the line crosses the y-axis. This value is found by setting x to zero in the equation.
Step-by-step explanation:
To find the y-intercept of the line y=8x–7, you need to determine the value of y when x is zero. In a linear equation of the form y=mx+b, where m is the slope and b is the y-intercept, the y-intercept can be identified as the constant term b. Looking at the equation y=8x–7, the slope, m, is 8, and the y-intercept, b, is –7. This indicates that the line crosses the y-axis at the point (0, -7).
To graphically illustrate this, plot the point (0, -7) on the y-axis and use the slope of 8 to rise 8 units for every 1 unit you move to the right along the x-axis. This creates a straight line that exhibits a consistent slope throughout, as is characteristic of linear equations. Applying this understanding allows us to clearly define the y-intercept as the starting point on the y-axis for any given line.