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The problem is asking for the equation of the line that passes through the points \((1, 5)\) and \((-2, 9)\). To find the equation in slope-intercept form (\(y = mx + b\)), we need to go through the following steps:

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

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

Substituting the given points \((1, 5)\) and \((-2, 9)\):

\[
m = \frac{9 - 5}{-2 - 1} = \frac{4}{-3} = -\frac{4}{3}
\]

### 2. Use the point-slope form to find the equation of the line:
The point-slope form of a line is:

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

We can use either of the points. Let's use \((1, 5)\) and the slope \(m = -\frac{4}{3}\):

\[
y - 5 = -\frac{4}{3}(x - 1)
\]

### 3. Simplify the equation:
Distribute the slope:

\[
y - 5 = -\frac{4}{3}x + \frac{4}{3}
\]

Add 5 to both sides to solve for \(y\):

\[
y = -\frac{4}{3}x + \frac{4}{3} + 5
\]

Convert 5 to a fraction with denominator 3:

\[
y = -\frac{4}{3}x + \frac{4}{3} + \frac{15}{3}
\]

\[
y = -\frac{4}{3}x + \frac{19}{3}
\]

### Final Equation:
The equation of the line in slope-intercept form is:

\[
y = -\frac{4}{3}x + \frac{19}{3}
\]

### 4. Slope of a parallel line:
For lines to be parallel, they must have the same slope. So, the slope of a line parallel to this one is also:

\[
m = -\frac{4}{3}
\]

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Do you want further details or have any questions? Here are some related questions to think about:

1. What is the difference between the slope-intercept form and point-slope form of a line?
2. How would the equation of the line change if we used \((-2, 9)\) to find it instead?
3. How do you calculate the y-intercept \(b\) directly if given two points?
4. What would the slope of a line perpendicular to this one be?
5. How can you verify if two lines are parallel or perpendicular?

**Tip:** Remember, parallel lines always have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other!

Write the equation of the line passing through the points (1, 5) and (−2, 9).

This problem covers how to find the equation of a line in slope-intercept form by calculating the slope and using point-slope form. It uses the points (1, 5) and (−2, 9), making it ideal for students in Grades 8-10.

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