if one point on a line is (5,-25) and the line's slope is -4, find the y intercept

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 \(x = 0\).

If one point on a line is (5,-25) and the line's slope is -4, find the y-intercept.

Learn how to find the y-intercept of a line with slope -4 passing through the point (5, -25). This problem uses key algebraic concepts such as the point-slope form and the slope-intercept theorem. Suitable for students in Grades 8-10.

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