A line passes through the points (-4,11) and (5,8). Write an equation of the line

To find the equation of the line that passes through the points \((-4, 11)\) and \((5, 8)\), we can follow these steps:

### Step 1: Find the Slope of the Line
The slope \(m\) of the line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

Substituting the given points \((-4, 11)\) and \((5, 8)\) into the formula:

\[
m = \frac{8 - 11}{5 - (-4)} = \frac{-3}{9} = -\frac{1}{3}
\]

### Step 2: Use the Point-Slope Form to Write the Equation
The point-slope form of the equation of a line is:

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

Substituting the slope \(m = -\frac{1}{3}\) and one of the points, say \((-4, 11)\), into the equation:

\[
y - 11 = -\frac{1}{3}(x + 4)
\]

### Step 3: Simplify to Get the Slope-Intercept Form
Simplify the equation to the slope-intercept form \(y = mx + b\):

\[
y - 11 = -\frac{1}{3}x - \frac{4}{3}
\]

Add \(11\) to both sides:

\[
y = -\frac{1}{3}x + \frac{-4 + 33}{3} = -\frac{1}{3}x + \frac{29}{3}
\]

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

\[
\boxed{y = -\frac{1}{3}x + \frac{29}{3}}
\]

Would you like further details on this or any specific part of the process? Here are some related questions you might find helpful:

1. How do you convert a linear equation from slope-intercept form to standard form?
2. What is the geometric interpretation of the slope of a line?
3. How do you find the y-intercept of a line if the equation is in point-slope form?
4. Can the slope of a line be zero or undefined? What does that imply?
5. How do you determine if two lines are parallel or perpendicular?
6. How do you find the distance between a point and a line?
7. How can you find the midpoint of a line segment given two points?
8. What is the general form of the equation of a line?

**Tip:** The slope is a measure of how steep a line is; a positive slope means the line is increasing, while a negative slope means the line is decreasing.

Learn how to write the equation of a line passing through the points (-4, 11) and (5, 8) using the slope-intercept form. Understand the calculation of slope, point-slope form, and converting to slope-intercept form step-by-step. Suitable for Grades 7-9 students studying geometry and linear equations.

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