Question

the equation of line c is $y - 5 = \frac{3}{5}(x - 7)$. parallel to line c is line d, which passes through the point $(1, -1)$. what is the equation of line d?
write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Identify the slope of line c

The equation of line c is in point - slope form \(y - y_1=m(x - x_1)\), where \(m\) is the slope. For the equation \(y - 5=\frac{3}{5}(x - 7)\), the slope \(m\) of line c is \(\frac{3}{5}\). Since parallel lines have the same slope, the slope of line d, \(m_d\), is also \(\frac{3}{5}\).

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

The point - slope form of a line is \(y - y_2=m(x - x_2)\), where \((x_2,y_2)=(1, - 1)\) and \(m = \frac{3}{5}\). Substitute these values into the formula:
\(y-(-1)=\frac{3}{5}(x - 1)\)
Simplify the left - hand side: \(y + 1=\frac{3}{5}(x - 1)\)

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

First, distribute the \(\frac{3}{5}\) on the right - hand side:
\(y + 1=\frac{3}{5}x-\frac{3}{5}\)
Then, subtract 1 from both sides. Recall that \(1=\frac{5}{5}\), so:
\(y=\frac{3}{5}x-\frac{3}{5}-\frac{5}{5}\)
\(y=\frac{3}{5}x-\frac{8}{5}\)

Answer:

\(y=\frac{3}{5}x-\frac{8}{5}\)