Select the correct answer.
Write the equation of a line that passes through the point
(5, 7)
and is perpendicular to the graph of
y = −
1
2
x +5
.
y = 2x − 17
y = 2x − 19
y = 2x −9
y = 2x −3
 answer

To solve this, we need to find the equation of a line that is perpendicular to the given line \( y = -\frac{1}{2}x + 5 \) and passes through the point \( (5, 7) \).

### Step 1: Find the slope of the perpendicular line
The slope of the given line is \( -\frac{1}{2} \). The slope of any line perpendicular to this will be the negative reciprocal of \( -\frac{1}{2} \), which is \( 2 \).

### Step 2: Use the point-slope form of a line equation
The point-slope form is:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope and \( (x_1, y_1) \) is the point through which the line passes. Plugging in the slope \( m = 2 \) and the point \( (5, 7) \), we get:
\[
y - 7 = 2(x - 5)
\]

### Step 3: Simplify the equation
\[
y - 7 = 2x - 10
\]
\[
y = 2x - 10 + 7
\]
\[
y = 2x - 3
\]

### Step 4: Conclusion
The equation of the line is \( y = 2x - 3 \), which matches the fourth option.

**Answer:** \( y = 2x - 3 \).

Would you like more details on any part of this process or have any questions?

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Here are 5 related questions to deepen understanding:
1. How do you find the slope of a line given two points?
2. What is the general process to find the equation of a line passing through two given points?
3. How do you calculate the negative reciprocal of a number?
4. What changes in the line equation if the line is parallel instead of perpendicular?
5. Can you explain how to verify that two lines are perpendicular using their slopes?

**Tip:** Remember, the slopes of perpendicular lines are always negative reciprocals of each other.

Write the equation of a line that passes through the point (5, 7) and is perpendicular to the graph of y = -1/2x + 5. y = 2x − 17, y = 2x − 19, y = 2x − 9, y = 2x − 3.

Learn how to find the equation of a line that passes through the point (5, 7) and is perpendicular to y = -1/2x + 5. This problem covers the point-slope formula and finding the slope of perpendicular lines. Suitable for Grades 8-10.

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