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.

1 answer

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:

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