Question

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

Explanation:

Step1: Find the slope of the perpendicular line

The slope of line \( w \) is \( -\frac{1}{2} \). The slope of a line perpendicular to it is the negative reciprocal, so \( m = 2 \).

Step2: Use point - slope form to find the equation

The point - slope form is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(1,1) \) and \( m = 2 \).
Substitute the values: \( y - 1 = 2(x - 1) \)

Step3: Simplify the equation

Expand the right - hand side: \( y - 1 = 2x - 2 \)
Add 1 to both sides: \( y = 2x - 1 \)

Answer:

The equation of the perpendicular line is \( y = 2x - 1 \)