Final answer:
The slope of the equation y=4x-8 is 4 and the y-intercept is (0, -8). To graph the equation, plot the y-intercept and use the slope to find another point; draw a line through the two points.
Step-by-step explanation:
To determine the slope and the y-intercept of the equation y=4x-8, you can compare it to the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept. In the given equation, the coefficient of x is 4, which is the slope. Therefore, the slope of the line is 4, which means for every increase of 1 on the horizontal axis, the value of y increases by 4 on the vertical axis. The constant term -8 is the y-intercept, indicating the point where the line crosses the y-axis. So, the y-intercept is (0, -8).
When graphing the equation, start at the y-intercept on the graph and use the slope to find another point. Since the slope is 4, from the y-intercept (0, -8), you would go up 4 units and 1 unit to the right to find another point on the line (1, -4). Draw the line through these two points, and this is the graph of the equation y=4x-8. You can use a graphing calculator to verify that the graph is a straight line that correctly represents the equation.