Question

line v has an equation of $y = -\frac{10}{9}x - 3$. perpendicular to line v is line w, which passes through the point (2, 3). what is the equation of line w? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Find the slope of line w

The slope of line v is $-\frac{10}{9}$. For perpendicular lines, the product of their slopes is -1. Let the slope of line w be $m$. Then $-\frac{10}{9} \times m = -1$. Solving for $m$, we get $m = \frac{9}{10}$.

Step2: Use point - slope form to find the equation

The point - slope form of a line is $y - y_1 = m(x - x_1)$, where $(x_1,y_1)=(2,3)$ and $m = \frac{9}{10}$. Substituting these values, we have $y - 3=\frac{9}{10}(x - 2)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y - 3=\frac{9}{10}x-\frac{18}{10}$. Then add 3 to both sides. Since $3=\frac{30}{10}$, we have $y=\frac{9}{10}x-\frac{18}{10}+\frac{30}{10}=\frac{9}{10}x+\frac{12}{10}=\frac{9}{10}x+\frac{6}{5}$.

Answer:

$y = \frac{9}{10}x+\frac{6}{5}$