Find the slope-intercept form of the equation of the line passing through the given points.(1, 1),   (7, -3/4)

To find the slope-intercept form of the equation of a line, \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).

### Step 1: Find the slope \( m \)
The slope \( m \) is given by the formula:

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

Using the points \( (1, 1) \) and \( (7, -\frac{3}{4}) \), assign:
- \( x_1 = 1 \), \( y_1 = 1 \)
- \( x_2 = 7 \), \( y_2 = -\frac{3}{4} \)

Substitute these values into the slope formula:

\[
m = \frac{-\frac{3}{4} - 1}{7 - 1} = \frac{-\frac{3}{4} - \frac{4}{4}}{6} = \frac{-\frac{7}{4}}{6} = \frac{-7}{24}
\]

So, the slope is \( m = -\frac{7}{24} \).

### Step 2: Use point-slope form to find the equation
Now that we know the slope \( m = -\frac{7}{24} \), use the point-slope form of the line equation:

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

Substitute \( m = -\frac{7}{24} \), \( x_1 = 1 \), and \( y_1 = 1 \):

\[
y - 1 = -\frac{7}{24}(x - 1)
\]

### Step 3: Simplify to slope-intercept form
Distribute the slope on the right side:

\[
y - 1 = -\frac{7}{24}x + \frac{7}{24}
\]

Add 1 to both sides to solve for \( y \):

\[
y = -\frac{7}{24}x + \frac{7}{24} + 1
\]

Convert 1 to a fraction with a denominator of 24:

\[
y = -\frac{7}{24}x + \frac{7}{24} + \frac{24}{24}
\]

Simplify the constant term:

\[
y = -\frac{7}{24}x + \frac{31}{24}
\]

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

\[
y = -\frac{7}{24}x + \frac{31}{24}
\]

Would you like further details or clarifications?

Here are 5 related questions:
1. How do you find the slope if the points involve negative coordinates?
2. How does the slope-intercept form compare to the standard form of a line?
3. What is the significance of the slope in real-world applications?
4. How would you graph the line given this equation?
5. How does the point-slope form relate to the slope-intercept form?

**Tip:** The slope of a line represents how steep the line is; a negative slope indicates that the line is decreasing as you move from left to right.

Find the slope-intercept form of the equation of the line passing through the given points (1, 1), (7, -3/4).

Learn how to find the slope-intercept form of a line passing through the points (1, 1) and (7, -3/4). This step-by-step solution covers key concepts such as the slope formula and converting point-slope form to slope-intercept form. Suitable for students in Grades 9-11.

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