find the equation of the line that has the coefficient of m=-1 and passes through the point (9,4) in slope interception form

To find the equation of a line in slope-intercept form, \( y = mx + b \), we need two things:

1. The slope \( m \), which is given as \( m = -1 \).
2. A point \((x_1, y_1)\) the line passes through, given as \( (9, 4) \).

We can substitute the values of \( m \), \( x_1 \), and \( y_1 \) into the slope-intercept form to solve for \( b \), the y-intercept.

Start with the equation:
\[
y = mx + b
\]
Substitute \( m = -1 \), \( x_1 = 9 \), and \( y_1 = 4 \) into the equation:
\[
4 = (-1)(9) + b
\]
This simplifies to:
\[
4 = -9 + b
\]
Add 9 to both sides to solve for \( b \):
\[
b = 13
\]

Now we can write the full equation of the line:
\[
y = -x + 13
\]

Thus, the equation of the line is \( y = -x + 13 \).

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How do you find the slope of a line given two points?
2. How does changing the slope affect the graph of a line?
3. What happens to the line when you change the y-intercept \( b \)?
4. How can you write the equation of a line in point-slope form?
5. Can a vertical line have a slope-intercept form?

**Tip:** The slope-intercept form is useful because it immediately shows both the slope and where the line crosses the y-axis.

Learn how to find the equation of a line with a slope of -1 that passes through the point (9,4) in slope-intercept form. This solution includes step-by-step algebraic methods, solving for the y-intercept, and writing the final equation of the line. Perfect for students in Grades 7-10.

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