Final answer:
The equation of the line with a slope of 3 and a y-intercept of 9 is expressed in slope-intercept form as y = 3x + 9.
Step-by-step explanation:
To write an equation for a graph in slope-intercept form, we need to identify the slope (m) and the y-intercept (b) of the line on the graph. The general equation for a line in slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. For the graph you've described, with a slope of 3 and a y-intercept of 9, the equation of the line is y = 3x + 9.
Let's break it down step-by-step:
- Slope (m): The graph shows a rise of 3 on the vertical axis for every increase of 1 on the horizontal axis. Therefore, the slope m is 3.
- Y-intercept (b): The graph intersects the y-axis at 9. This means the y-intercept b is 9.
Putting it all together, you substitute the values of m and b into the slope-intercept form equation, giving us y = 3x + 9 as the final equation representing the graphed line.