To convert the equation from point-slope form to slope-intercept form, we'll simplify and rearrange the equation.

Step 1: Start with the point-slope form

We have: $y - 2 = \frac{2}{11}(x - 7)$

Step 2: Distribute the slope

Distribute $\frac{2}{11}$ to both terms inside the parentheses: $y - 2 = \frac{2}{11}x - \frac{14}{11}$

Step 3: Isolate $y$

Add 2 to both sides to solve for $y$: $y = \frac{2}{11}x - \frac{14}{11} + 2$

Step 4: Combine the constant terms

Convert 2 to a fraction with a denominator of 11: $2 = \frac{22}{11}$ So the equation becomes: $y = \frac{2}{11}x - \frac{14}{11} + \frac{22}{11}$ $y = \frac{2}{11}x + \frac{8}{11}$

Final Answer

The slope-intercept form of the equation is: $y = \frac{2}{11}x + \frac{8}{11}$

This equation is now in the form $y = mx + b$, where $m = \frac{2}{11}$ is the slope, and $b = \frac{8}{11}$ is the y-intercept.

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Related Questions:

1. How do you determine the y-intercept from a graph?
2. What does the slope $m$ represent in the context of a linear equation?
3. How would the equation change if the slope were negative?
4. How can you quickly graph a line using its slope-intercept form?
5. What are some real-world applications of linear equations in slope-intercept form?

Tip:

When working with fractions in slope-intercept form, ensure to simplify them when possible to make the equation easier to interpret and use.