The slope-intercept form of a linear equation is given by:

$y = mx + b$

where:

• $m$ is the slope of the line,
• $b$ is the y-intercept, which is the point where the line crosses the y-axis.

Given:

• Slope $m = 3$,
• Y-intercept $b = 5$ (from the point $(0, 5)$).

Substitute these values into the slope-intercept equation:

$y = 3x + 5$

Final Answer:

The equation of the line is:

$y = 3x + 5$

Would you like more details or have any questions?

Here are 8 related questions you might consider:

1. How do you find the slope of a line given two points?
2. What is the equation of a line with a slope of -2 and a y-intercept of 3?
3. How do you convert a standard form equation to slope-intercept form?
4. What is the significance of the slope in the context of a graph?
5. How do you find the equation of a line parallel to $y = 3x + 5$?
6. How do you find the equation of a line perpendicular to $y = 3x + 5$?
7. What is the slope-intercept form for a horizontal line?
8. How does the y-intercept change if the line passes through the origin?

Tip: When identifying the equation of a line, always pay attention to the slope and y-intercept as they directly determine the line's behavior and position on the graph.