Give the equation of the line passing through the point (5,−14)(5,-14) that is parallel to y=−2x+3y=-2x+3.

Write your answer in Slope-Intercept Form.

To find the equation of the line that is parallel to the line \( y = -2x + 3 \) and passes through the point \( (5, -14) \), follow these steps:

### 1. Determine the slope of the parallel line.
The slope of the given line \( y = -2x + 3 \) is \( m = -2 \). Since parallel lines have the same slope, the slope of the new line will also be \( m = -2 \).

### 2. Use the point-slope form of the equation.
The point-slope form is:

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

Here, \( m = -2 \) and the point \( (x_1, y_1) \) is \( (5, -14) \). Plugging in these values:

\[
y + 14 = -2(x - 5)
\]

### 3. Simplify to slope-intercept form.
Distribute the slope \( -2 \):

\[
y + 14 = -2x + 10
\]

Now, subtract 14 from both sides to solve for \( y \):

\[
y = -2x - 4
\]

### Final Answer:
The equation of the line in slope-intercept form is:

\[
\boxed{y = -2x - 4}
\]

Would you like more details or have any questions? Here are five related questions to consider:

1. How do you determine if two lines are parallel?
2. What are the characteristics of parallel lines in terms of their slopes?
3. Can you find the distance between two parallel lines?
4. How do you find the equation of a line given its slope and a point?
5. What is the significance of the y-intercept in the equation of a line?

**Tip:** Remember, parallel lines always have identical slopes, which means their equations differ only by the y-intercept.

Learn how to find the equation of a line parallel to y = -2x + 3 that passes through the point (5, -14). This problem involves using the point-slope form of a line equation and understanding parallel lines in geometry. Suitable for students in Grades 7-9.

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