To find the y-intercept of a line when you know one point on the line and the slope, you can use the point-slope form of the line equation:

$y - y_1 = m(x - x_1)$

where:

• $(x_1, y_1)$ is a point on the line,
• $m$ is the slope.

Given:

• The point $(5, -25)$,
• The slope $m = -4$.

Substituting the values into the equation:

$y - (-25) = -4(x - 5)$

Simplify this equation:

$y + 25 = -4x + 20$

Now, solve for $y$:

$y = -4x + 20 - 25$

$y = -4x - 5$

The y-intercept is the constant term when the equation is in the form $y = mx + b$. Therefore, the y-intercept $b$ is:

$b = -5$

The y-intercept of the line is $-5$.

Would you like to see more details or have any questions? Here are some related questions to expand on this topic:

1. How do you find the slope of a line given two points?
2. What is the point-slope form, and how does it differ from the slope-intercept form?
3. How can you determine if two lines are parallel or perpendicular?
4. How do you find the equation of a line given a point and a y-intercept?
5. How can you graph a line using its slope and y-intercept?

Tip: Remember, the y-intercept is where the line crosses the y-axis, meaning $x = 0$.