Question

write the equation of the line that is perpendicular to $y = \frac{4}{5}x - 1$ and passes through (4, 3). use the point - slope form: $y - y_1 = m(x - x_1)$

1. $m =$ - 5/4 perpendicular slope
2. $b =$ 8 y - intercept
3. equation = type your answer... $y = mx + b$

Explanation:

Step1: Recall slope of perpendicular line

The slope of the given line \( y = \frac{4}{5}x - 1 \) is \( \frac{4}{5} \). The slope of a line perpendicular to it is the negative reciprocal, so \( m = -\frac{5}{4} \).

Step2: Use point - slope form to find equation

Using point - slope form \( y - y_1 = m(x - x_1) \) with \( (x_1,y_1)=(4,3) \) and \( m = -\frac{5}{4} \):
\( y - 3=-\frac{5}{4}(x - 4) \)

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y - 3=-\frac{5}{4}x + 5 \)
Add 3 to both sides: \( y=-\frac{5}{4}x+5 + 3 \)
\( y = -\frac{5}{4}x+8 \)
So the slope \( m = -\frac{5}{4} \), the y - intercept \( b = 8 \), and the equation is \( y=-\frac{5}{4}x + 8 \)

Answer:

1. \( m = -\frac{5}{4} \)
2. \( b = 8 \)
3. Equation \( = y=-\frac{5}{4}x + 8 \)