Question

the equation for line s can be written as $y - 8 = \frac{1}{7}(x - 1)$. line t, which is parallel to line s, includes the point $(10, 2)$. 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.

Explanation:

Step1: Determine the slope of line t

Parallel lines have the same slope. The equation of line \( s \) is in point - slope form \( y - y_1=m(x - x_1) \), where \( m \) is the slope. For the equation \( y - 8=\frac{1}{7}(x - 1) \), the slope \( m \) of line \( s \) is \( \frac{1}{7} \). So the slope of line \( t \), which is parallel to line \( s \), is also \( m=\frac{1}{7} \).

Step2: Use the point - slope form to find the equation of line t

The point - slope form of a line is \( y - y_2=m(x - x_2) \), where \( (x_2,y_2)=(10,2) \) is a point on line \( t \) and \( m = \frac{1}{7} \). Substitute these values into the point - slope form:
\( y - 2=\frac{1}{7}(x - 10) \)

Step3: Convert to slope - intercept form (\( y=mx + b \))

First, distribute the \( \frac{1}{7} \) on the right - hand side:
\( y - 2=\frac{1}{7}x-\frac{10}{7} \)
Then, add 2 to both sides of the equation. We can write 2 as \( \frac{14}{7} \) to have a common denominator:
\( y=\frac{1}{7}x-\frac{10}{7}+\frac{14}{7} \)
Simplify the right - hand side:
\( y=\frac{1}{7}x+\frac{- 10 + 14}{7}=\frac{1}{7}x+\frac{4}{7} \)

Answer:

\( y=\frac{1}{7}x+\frac{4}{7} \)