To find the equation of a line in slope-intercept form, $y = mx + b$, we need the slope $m$ and the y-intercept $b$.

Given:

• Point: $(4, 1)$
• Slope: $m = -\frac{5}{4}$

Steps:

1. Use the point-slope form of the equation of a line:
   $y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is a point on the line.

2. Substitute the given point $(4, 1)$ and the slope $-\frac{5}{4}$: $y - 1 = -\frac{5}{4}(x - 4)$

3. Expand the equation: $y - 1 = -\frac{5}{4}x + \frac{5}{4} \cdot 4$ $y - 1 = -\frac{5}{4}x + 5$

4. Solve for $y$ to put the equation in slope-intercept form: $y = -\frac{5}{4}x + 5 + 1$ $y = -\frac{5}{4}x + 6$

Final Answer:

The equation of the line in slope-intercept form is: $y = -\frac{5}{4}x + 6$

Would you like more details on any part of this process?

Here are five related questions for further exploration:

1. How do you find the equation of a line given two points instead of a point and a slope?
2. What does the slope of a line represent geometrically?
3. How can you determine if two lines are parallel or perpendicular?
4. How do you convert a line equation from slope-intercept form to standard form?
5. How do you find the x-intercept of a line given its slope-intercept equation?

Tip: In slope-intercept form, the coefficient of $x$ represents the slope, and the constant term represents the y-intercept directly.