Question

Line u has an equation of y–5=2(x–5). Line v includes the point (
–
2,
–
3) and is parallel to line u. What is the equation of line v?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answer 1

To find the equation of line \( v \), we first need to determine the slope of line \( u \) from its equation.

The equation of line \( u \) is given in point-slope form:
\[
y - 5 = 2(x - 5)
\]
From this equation, we can see that the slope \( m \) of line \( u \) is \( 2 \).

Since line \( v \) is parallel to line \( u \), it will have the same slope. Therefore, the slope of line \( v \) is also \( 2 \).

Next, we can use the point-slope form of the equation of a line to find the equation of line \( v \). Line \( v \) passes through the point \( (-2, -3) \) and has a slope of \( 2 \). The point-slope form is given by:

\[
y - y_1 = m(x - x_1)
\]
Plugging in \( m = 2 \), \( x_1 = -2 \), and \( y_1 = -3 \):
\[
y - (-3) = 2(x - (-2))
\]
This simplifies to:
\[
y + 3 = 2(x + 2)
\]

Now, distribute the \( 2 \):
\[
y + 3 = 2x + 4
\]

Next, we subtract \( 3 \) from both sides to put the equation in slope-intercept form \( y = mx + b \):
\[
y = 2x + 4 - 3
\]
\[
y = 2x + 1
\]

Thus, the equation of line \( v \) in slope-intercept form is:
\[
\boxed{y = 2x + 1}
\]