Question

what is the equation in slope - intercept form of the line that passes through the point (6, 3) and is parallel to the graph of $y = \frac{2}{3}x + 12$?
$y = \square x + \square$

Explanation:

Step1: Determine the slope

Parallel lines have the same slope. The given line is \( y = -\frac{2}{3}x + 12 \), so the slope \( m = -\frac{2}{3} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(6,3) \) and \( m = -\frac{2}{3} \).
Substitute the values: \( y - 3=-\frac{2}{3}(x - 6) \)

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y - 3=-\frac{2}{3}x+4 \)
Add 3 to both sides: \( y=-\frac{2}{3}x + 4+3 \)
Simplify: \( y = -\frac{2}{3}x+7 \)

Answer:

\( y = -\frac{2}{3}x + 7 \)