Final answer:
The equation y=3x+5 means that the slope of the line is 3, and the y-intercept is 5. The slope tells us how much y increases for a unit increase in x, and the y-intercept is the point where the line crosses the y-axis. Thus, the correct answer is A) Slope = 3, y-intercept = 5.
Step-by-step explanation:
Understanding the Slope and Y-Intercept
When dealing with linear equations, understanding the slope and y-intercept is fundamental. For the equation y = 3x + 5, 3 represents the slope, and 5 is the y-intercept. The slope, 3, indicates that for every increase of 1 on the horizontal axis, the value of y increases by 3 on the vertical axis. The y-intercept, which is 5, is the point where the line crosses the y-axis. This means that when x = 0, y will equal 5.
In this context, the correct answer is A) Slope = 3, y-intercept = 5.
To accurately identify the slope and y-intercept from an equation, remember that in the slope-intercept form (y = mx + b), m stands for the slope and b represents the y-intercept. Therefore, comparing the given equation y = 3x + 5 with the slope-intercept form, it’s clear that the coefficient of x, which is 3, is the slope, and the constant term, which is 5, is the y-intercept.