Write an equation in point-slope form of the line that passes through the point  $\left(5,\ -12\right)$   and has a slope of  $m=-\frac{2}{5}$
 .
$y-$ 
  $=$  
 $\text{(}x-$ 
 $\text{)}$

Question 2
Graph the line.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -10.4 to 10.4 with ticks spaced every 1 unit(s).
The vertical axis goes from -20.4 to 8.4 with ticks spaced every 2 unit(s).


To write the equation of a line in point-slope form, we use the formula:

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

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

Given:
- Point: $(x_1, y_1) = (5, -12)$
- Slope: $m = -\frac{2}{5}$

Substitute these values into the formula:

\[
y - (-12) = -\frac{2}{5}(x - 5)
\]

Simplify:

\[
y + 12 = -\frac{2}{5}(x - 5)
\]

The equation in point-slope form is:

\[
y + 12 = -\frac{2}{5}(x - 5)
\]

### Graphing the Line
To graph this line, you could:
1. Start at the point $(5, -12)$.
2. Use the slope $-\frac{2}{5}$, which means move down 2 units and right 5 units to find another point.
3. Draw the line through these points.

Would you like more details, or do you have questions?

---

**Related Questions:**
1. What is the general form of a linear equation?
2. How do you convert from point-slope form to slope-intercept form?
3. What does the slope represent in a real-world context?
4. How do you graph a line given a point and a slope?
5. How can you check if a point lies on a given line?

**Tip:** In point-slope form, the point used does not have to be on the y-axis, making it very flexible for any point on the line.

Write an equation in point-slope form of the line that passes through the point (5, -12) and has a slope of m = -2/5. Then, graph the line.

Learn how to write an equation in point-slope form for a line that passes through the point (5, -12) with a slope of -2/5. This lesson covers linear equation concepts and includes steps for graphing the line. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation