Question

1. m = -1

(graph with x-axis from -6 to 6, y-axis from -6 to 6, a dot at (3,3))
m = ____ b = ____
equation: ______

Explanation:

Step1: Identify the given slope and point

The slope \( m = -1 \), and the point on the line is \( (3, 3) \) (from the graph, the dot is at \( x = 3 \), \( y = 3 \)).

Step2: Use the point - slope form \( y - y_1 = m(x - x_1) \)

Substitute \( m=-1 \), \( x_1 = 3 \), and \( y_1 = 3 \) into the formula:
\( y - 3=-1(x - 3) \)

Step3: Simplify to slope - intercept form \( y=mx + b \)

Expand the right - hand side: \( y - 3=-x + 3 \)
Add 3 to both sides: \( y=-x+3 + 3\), so \( y=-x + 6 \)
Here, the slope \( m=-1 \) (given), and the y - intercept \( b = 6 \) (from the equation \( y=-x + 6 \), where the form is \( y=mx + b \))

Answer:

\( m=-1 \), \( b = 6 \), Equation: \( y=-x + 6 \)