write the slope-intercept form of the equation of the line through the given points
through: (4,-1) and (0,0)

To find the slope-intercept form of the equation of a line, we follow these steps:

### 1. Find the slope (m):
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( (4, -1) \) and \( (0, 0) \):

\[
m = \frac{0 - (-1)}{0 - 4} = \frac{1}{-4} = -\frac{1}{4}
\]

### 2. Use the slope-intercept form:
The slope-intercept form of a line is:

\[
y = mx + b
\]

We know the slope \( m = -\frac{1}{4} \) and that the line passes through the point \( (0, 0) \), which is the y-intercept, so \( b = 0 \).

### 3. Write the equation:
Now that we have the slope and intercept, the equation of the line is:

\[
y = -\frac{1}{4}x
\]

This is the slope-intercept form of the equation of the line passing through the points \( (4, -1) \) and \( (0, 0) \).

Would you like more details on this process, or have any questions?

Here are some related questions to expand your understanding:
1. What would be the equation of the line if the points were different, such as \( (2, 3) \) and \( (6, 1) \)?
2. How do you find the equation of a line given its slope and a point?
3. What is the significance of the slope in the graph of a line?
4. How would the equation change if the line had a different y-intercept?
5. How do you convert between slope-intercept form and standard form?

**Tip:** A slope of \( -\frac{1}{4} \) means for every 4 units you move horizontally to the right, the line drops 1 unit vertically.

write the slope-intercept form of the equation of the line through the given points through: (4,-1) and (0,0)

Learn how to find the slope-intercept form of the line that passes through the points (4,-1) and (0,0). This example covers algebraic concepts such as the slope formula and slope-intercept form. Suitable for students in Grades 8-10.

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