Use point-slope form to write the equation of a line that passes through the point left parenthesis, 10, comma, minus, 16, right parenthesis(10,−16) with slope 22.

The point-slope form of the equation of a line is given by:

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

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

In this case, we have the point \((10, -16)\) and the slope \(m = 22\). Plugging these values into the formula:

\[
y - (-16) = 22(x - 10)
\]

Simplifying this equation:

\[
y + 16 = 22(x - 10)
\]

To convert this into slope-intercept form (optional), you can distribute and simplify further:

\[
y + 16 = 22x - 220
\]
\[
y = 22x - 220 - 16
\]
\[
y = 22x - 236
\]

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

\[
y + 16 = 22(x - 10)
\]

And in slope-intercept form:

\[
y = 22x - 236
\]

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. What is the equation of a line passing through the point \((4, 5)\) with slope \(3\)?
2. How do you convert point-slope form to slope-intercept form?
3. What is the slope of a line parallel to the line \(y = 7x + 1\)?
4. Find the slope of a line passing through points \((2, 3)\) and \((6, -1)\).
5. Write the equation of a line perpendicular to \(y = -\frac{1}{2}x + 4\) and passing through \((0, 0)\).

**Tip:** Always make sure to distribute carefully when converting from point-slope to slope-intercept form!

Use point-slope form to write the equation of a line that passes through the point (10, −16) with slope 22.

Learn how to write the equation of a line using point-slope form. This problem involves writing an equation for a line that passes through the point (10, -16) with a slope of 22 and converting it to slope-intercept form. Suitable for students in Grades 8-10.

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