Question

Write an equation in​ slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
​(minus7​,minus8​); y equals negative 2 x plus 4
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Part 1
Write an equation for the line in​ slope-intercept form.

Answer 1

To find the equation of a line that is parallel to a given line and passes through a specified point, we need to follow these steps:

1. **Identify the slope of the given line**: The equation provided is \( y = -2x + 4 \). The slope \( m \) of this line is \(-2\).

2. **Use the same slope for the new line**: Since the new line must be parallel to the given line, it will have the same slope. Therefore, the slope of the new line will also be \(-2\).

3. **Use the point-slope form to find the equation**: We will use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is the point through which the line passes and \( m \) is the slope. We will use the point \((-7, -8)\).

Plugging in the values:
\[
y - (-8) = -2(x - (-7))
\]
This simplifies to:
\[
y + 8 = -2(x + 7)
\]

4. **Distribute and isolate \( y \)**:
\[
y + 8 = -2x - 14
\]
\[
y = -2x - 14 - 8
\]
\[
y = -2x - 22
\]

Thus, the equation of the line in slope-intercept form is:
\[
\boxed{y = -2x - 22}
\]