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: Identify parallel line slope

Parallel lines have equal slopes. Line $s$ is in point-slope form $y-y_1=m(x-x_1)$, so slope $m=\frac{1}{7}$.

Step2: Use point-slope for line $t$

Substitute $m=\frac{1}{7}$ and point $(10,2)$ into point-slope form:
$y - 2 = \frac{1}{7}(x - 10)$

Step3: Convert to slope-intercept form

Expand and solve for $y$:
$y - 2 = \frac{1}{7}x - \frac{10}{7}$
$y = \frac{1}{7}x - \frac{10}{7} + 2$
$y = \frac{1}{7}x - \frac{10}{7} + \frac{14}{7}$
$y = \frac{1}{7}x + \frac{4}{7}$

Answer:

$y = \frac{1}{7}x + \frac{4}{7}$