Use point-slope form to write the equation of a line that passes through the point left parenthesis, 14, comma, minus, 17, right parenthesis(14,−17) with slope minus, 2−2.

The point-slope form of a line is written as:

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

Where:
- \((x_1, y_1)\) is a point on the line
- \(m\) is the slope of the line

In your case, the point is \((14, -17)\) and the slope is \(-2\).

Substitute the values into the formula:

\[
y - (-17) = -2(x - 14)
\]

Simplifying the equation:

\[
y + 17 = -2(x - 14)
\]

Now distribute the slope:

\[
y + 17 = -2x + 28
\]

Finally, subtract 17 from both sides to solve for \(y\):

\[
y = -2x + 28 - 17
\]

\[
y = -2x + 11
\]

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

\[
y = -2x + 11
\]

Would you like further details or explanations? Here are some related questions:

1. How do you convert point-slope form to slope-intercept form?
2. What is the general form of a linear equation, and how can we convert to it?
3. How do you find the slope of a line given two points?
4. How can the slope help determine if two lines are parallel or perpendicular?
5. What is the significance of the y-intercept in the equation of a line?

**Tip:** Point-slope form is especially useful when you know a point on the line and the slope, as it quickly gives the equation without needing to find the y-intercept directly.

Use point-slope form to write the equation of a line that passes through the point (14,−17) with slope −2.

Learn how to use point-slope form to write the equation of a line passing through the point (14,−17) with a slope of −2. This step-by-step guide simplifies the process of converting the equation into slope-intercept form. Suitable for students in Grades 8-10.

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