Question

the equation for line w, graphed below, is $y = -\frac{2}{5}x + 4$. create a consistent system of linear equations by graphing a line perpendicular to line w that passes through (1, -8).

Explanation:

Step1: Find the slope of the perpendicular line

The slope of line \( w \) is \( -\frac{2}{5} \). The slope of a line perpendicular to it is the negative reciprocal, so \( m = \frac{5}{2} \).

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 \( (x_1,y_1)=(1, - 8) \) and \( m=\frac{5}{2} \).
Substitute the values: \( y - (-8)=\frac{5}{2}(x - 1) \)
Simplify: \( y + 8=\frac{5}{2}x-\frac{5}{2} \)
Subtract 8 from both sides: \( y=\frac{5}{2}x-\frac{5}{2}-8 \)
\( y=\frac{5}{2}x-\frac{5 + 16}{2} \)
\( y=\frac{5}{2}x-\frac{21}{2} \)

Answer:

The equation of the perpendicular line is \( y=\frac{5}{2}x-\frac{21}{2} \)