https://file.aiquickdraw.com/mathbot/file/1725568051104fpmg75a1.jpg

To solve problem 3, which asks to determine the slope-intercept form of the line that passes through the points \( (3, 9) \) and \( (1, 10) \), we can follow these steps:

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

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

Substitute the given points \( (3, 9) \) and \( (1, 10) \):

\[
m = \frac{10 - 9}{1 - 3} = \frac{1}{-2} = -\frac{1}{2}
\]

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

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

We can use either point, but let's use \( (1, 10) \). Substituting the values into the formula:

\[
y - 10 = -\frac{1}{2}(x - 1)
\]

### Step 3: Simplify to slope-intercept form
Now, distribute the slope on the right-hand side:

\[
y - 10 = -\frac{1}{2}x + \frac{1}{2}
\]

Add 10 to both sides to isolate \( y \):

\[
y = -\frac{1}{2}x + \frac{1}{2} + 10
\]

Simplify:

\[
y = -\frac{1}{2}x + \frac{21}{2}
\]

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

\[
y = -\frac{1}{2}x + \frac{21}{2}
\]

Would you like a detailed explanation on any of the steps or have additional questions?

Here are some related questions to deepen your understanding:

1. How would the equation change if the points were reversed?
2. What is the significance of the slope in this context?
3. How do we convert this equation into standard form?
4. What happens if the slope is zero? How does the equation look?
5. How can you verify that both points satisfy the equation?

**Tip:** Always double-check your slope calculation by ensuring the difference in \( y \)-values and \( x \)-values are consistent across both points.

Solve problem 3 from the provided image, which asks to determine the slope-intercept form of the line that passes through the points (3, 9) and (1, 10).

Learn how to find the slope-intercept form of a line passing through the points (3, 9) and (1, 10). This problem involves calculating the slope and applying the point-slope formula to convert to slope-intercept form. 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