Question

Find the equation of the line parallel to.
y, equals, minus, start fraction, 3, divided by, 5, end fraction, x, plus, 4, .y=−
5
3
​
x+4
and going through the point. , left parenthesis, minus, 10, comma, minus, 6, right parenthesis, .
(−10,−6)

your answer should be in slope intercept form. , y, equals, m, x, plus, b
y=mx+b

Answer 1

To find the equation of a line that is parallel to the given line \( y = -\frac{3}{5}x + 4 \) and passes through the point \((-10, -6)\), we can use the following steps:

1. **Identify the slope of the given line**: The slope \( m \) of the line \( y = -\frac{3}{5}x + 4 \) is \(-\frac{3}{5}\). Since parallel lines have the same slope, the slope of our new line will also be \(-\frac{3}{5}\).

2. **Use point-slope form**: We can use the point-slope form of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is the point the line passes through and \( m \) is the slope.

Here, \( (x_1, y_1) = (-10, -6) \) and \( m = -\frac{3}{5} \).

3. **Substitute the values**:
\[
y - (-6) = -\frac{3}{5}(x - (-10))
\]
This simplifies to:
\[
y + 6 = -\frac{3}{5}(x + 10)
\]

4. **Distribute the slope**:
\[
y + 6 = -\frac{3}{5}x - \frac{3}{5} \cdot 10
\]
\[
y + 6 = -\frac{3}{5}x - 6
\]

5. **Subtract 6 from both sides**:
\[
y = -\frac{3}{5}x - 6 - 6
\]
\[
y = -\frac{3}{5}x - 12
\]

Thus, the equation of the line that is parallel to the given line and passes through the point \((-10, -6)\) in slope-intercept form is:
\[
\boxed{y = -\frac{3}{5}x - 12}
\]