write an equation of the line that passes through (8,2) And is perpendicular to the line who equation is -1/2x+3

The equation of the line given is:

\[
y = -\frac{1}{2}x + 3
\]

Since the new line is perpendicular to this one, its slope will be the negative reciprocal of the slope of the original line. The slope of the given line is \(-\frac{1}{2}\), so the slope of the perpendicular line will be:

\[
m = 2
\]

Now, we need to find the equation of the line that has this slope \(m = 2\) and passes through the point \((8, 2)\). Using the point-slope form of a line equation, which is:

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

where \((x_1, y_1)\) is the point \((8, 2)\), we can substitute the values:

\[
y - 2 = 2(x - 8)
\]

Simplifying this:

\[
y - 2 = 2x - 16
\]

\[
y = 2x - 14
\]

Thus, the equation of the line is:

\[
y = 2x - 14
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you find the slope of a line between two points?
2. What does it mean for two lines to be parallel?
3. How can you find the y-intercept of a line given its equation?
4. What is the slope-intercept form of a line equation?
5. How do you write the equation of a line given its slope and one point?

**Tip:** When two lines are perpendicular, their slopes multiply to \(-1\).

write an equation of the line that passes through (8,2) and is perpendicular to the line whose equation is -1/2x+3

Learn how to write the equation of a line that passes through the point (8,2) and is perpendicular to the line y = -1/2x + 3. This step-by-step solution explains how to find the slope of the perpendicular line, use the point-slope form, and simplify the equation. Suitable for students in Grades 8-10.

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