Question

question 2
1 pts
given the line $y = \frac{2}{7}x + 1$ find the equation of a line that is parallel to it while passing through the point $(3, 5)$.
write your final answer in the slope - intercept form $y = mx + b$ in the box provided below. if the coefficient of $x$ in your answer is a fraction, enter your equation in the form $y=(a/k)x + b$, and where applicable, the $b$ term must also be entered in fraction form.

Explanation:

Step1: Identify slope of parallel line

Parallel lines have equal slopes. The given line is \( y = \frac{2}{7}x + 1 \), so the slope \( m \) of the parallel line is \( \frac{2}{7} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(3,5) \) and \( m = \frac{2}{7} \). Substitute these values: \( y - 5=\frac{2}{7}(x - 3) \).

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y - 5=\frac{2}{7}x-\frac{6}{7} \). Then add 5 to both sides. Since \( 5=\frac{35}{7} \), we have \( y=\frac{2}{7}x-\frac{6}{7}+\frac{35}{7} \). Combine the fractions: \( y=\frac{2}{7}x+\frac{35 - 6}{7}=\frac{2}{7}x+\frac{29}{7} \).

Answer:

\( y=\frac{2}{7}x+\frac{29}{7} \)