Answer:
[tex]y = -\frac{7}{10}x + \frac{4}{5}[/tex]
Step-by-step explanation:
Parallel lines have the same slope.
Given that line s is represented by the linear equation, [tex]y = -\frac{7}{10}x - 1[/tex], then line t must have the same slope of [tex]-\frac{7}{10}[/tex].
All we have to do at this point is use line t's slope, m = [tex]-\frac{7}{10}[/tex], and the given point, (-6, 5), to solve for the y-intercept, b:
y = mx + b
[tex]5 = -\frac{7}{10}(-6) + b[/tex]
[tex]5 = \frac{42}{10} + b[/tex]
[tex]5 = \frac{21}{5} + b[/tex]
Subtract [tex]\frac{21}{5}[/tex] from both sides:
[tex]5 - \frac{21}{5} = \frac{21}{5} - \frac{21}{5} + b[/tex]
[tex]\frac{4}{5}[/tex] = b
Therefore, the equation of line t that is parallel to line s is: [tex]y = -\frac{7}{10}x + \frac{4}{5}[/tex].
