A line has a slope of 
–
5 and passes through the point (1,
–
9). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.

To write the equation of a line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we need to use the given slope and the point through which the line passes.

### Given:
- Slope \( m = -5 \)
- Point \( (1, -9) \)

We will substitute the point \( (x_1, y_1) = (1, -9) \) and the slope \( m = -5 \) into the point-slope form equation:

\[
y - y_1 = m(x - x_1)
\]

Substitute the values:

\[
y - (-9) = -5(x - 1)
\]

Simplify the equation:

\[
y + 9 = -5(x - 1)
\]

Now distribute the \( -5 \):

\[
y + 9 = -5x + 5
\]

Next, isolate \( y \) by subtracting 9 from both sides:

\[
y = -5x + 5 - 9
\]

Simplify the right-hand side:

\[
y = -5x - 4
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = -5x - 4
\]

### Do you want more details or have any questions?

Here are 5 questions to deepen understanding:
1. How would the equation change if the slope were positive instead of negative?
2. What is the significance of the slope in the equation?
3. How can we find the y-intercept algebraically from the point and slope?
4. How do you graph a line using slope-intercept form?
5. How would the equation change if the line passed through a different point?

**Tip**: Always check your final equation by substituting the given point back into the equation to ensure it satisfies the line equation!

A line has a slope of -5 and passes through the point (1, -9). Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

Learn how to write the equation of a line with a slope of -5 that passes through the point (1, -9). This problem demonstrates key concepts like slope-intercept form and point-slope form, suitable for students in Grades 8-10.

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