Question

1. a line that has a slope of -5 and passes through the point (9, -3).

find the slope: m =
point - slope:
slope - intercept:
standard:

Explanation:

Step1: Determine the slope

The problem states the slope of the line is -5, so \( m = -5 \).

Step2: Write the point - slope form

The point - slope formula is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(9,-3) \) and \( m=-5 \). Substituting these values, we get \( y - (-3)=-5(x - 9) \), which simplifies to \( y + 3=-5(x - 9) \).

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

Start with the point - slope form \( y + 3=-5(x - 9) \).
Expand the right - hand side: \( y+3=-5x + 45 \).
Subtract 3 from both sides: \( y=-5x+45 - 3 \), so \( y=-5x + 42 \).

Step4: Convert to standard form (\( Ax+By = C \), where \( A,B,C \) are integers and \( A\geq0 \))

Start with the slope - intercept form \( y=-5x + 42 \).
Add \( 5x \) to both sides: \( 5x+y=42 \).

Answer:

• Find the slope: \( m=-5 \)
• Point - Slope: \( y + 3=-5(x - 9) \)
• Slope - intercept: \( y=-5x + 42 \)
• Standard: \( 5x + y=42 \)