Question

Which equation represents a line which is parallel to the line y, equals, minus, start fraction, 8, divided by, 5, end fraction, x, minus, 1y=−
5
8
​
x−1?

Answer 1

To find a line that is parallel to the given line \( y = -\frac{8}{5}x - 1 \), we need to identify the slope of the original line. The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope.

From the equation \( y = -\frac{8}{5}x - 1 \), the slope \( m \) is:

\[
m = -\frac{8}{5}
\]

Lines that are parallel to each other have the same slope. Therefore, any line that has a slope of \( -\frac{8}{5} \) will be parallel to the given line.

The general equation of a line can be written as:

\[
y = -\frac{8}{5}x + b
\]

where \( b \) is the y-intercept, which can be any value.

For example, you could choose \( b = 0 \) to get the equation of a parallel line:

\[
y = -\frac{8}{5}x
\]

Or you can choose any other value for \( b \) (like \( b = 2 \), for instance):

\[
y = -\frac{8}{5}x + 2
\]

In conclusion, any equation of the form:

\[
y = -\frac{8}{5}x + b
\]

(where \( b \) is any real number) will represent a line parallel to the original line.