Question

The equation for line s can be written as y=
–
10x+
5
4
. Parallel to line s is line t, which passes through the point (
–
1,3). What is the equation of line t?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answer 1

To find the equation of line \( t \), which is parallel to line \( s \), we need to identify the slope of line \( s \) from its equation and then use that same slope for line \( t \).

The equation of line \( s \) is given as:

\[
y = -10x + \frac{5}{4}
\]

From this equation, we can see that the slope (\( m \)) of line \( s \) is \( -10 \).

Since line \( t \) is parallel to line \( s \), it will have the same slope. Therefore, line \( t \) also has a slope of \( -10 \).

Next, we use the point through which line \( t \) passes, which is \((-1, 3)\), to write the equation of line \( t \) using point-slope form:

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

Substituting in the values for \( m \), \( x_1 \), and \( y_1 \):

\[
y - 3 = -10(x - (-1))
\]
\[
y - 3 = -10(x + 1)
\]

Now, let's simplify this equation:

\[
y - 3 = -10x - 10
\]
\[
y = -10x - 10 + 3
\]
\[
y = -10x - 7
\]

Thus, the equation of line \( t \) in slope-intercept form is:

\[
\boxed{y = -10x - 7}
\]