Question

21
m = -2
(-4, 3)

Explanation:

Assuming we need to find the equation of a line with slope \( m = -2 \) and passing through the point \( (-4, 3) \). We use the point - slope form of a line's equation, which is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1) \) is the given point and \( m \) is the slope.

Step 1: Identify the values

We know that \( m=-2 \), \( x_1 = - 4 \) and \( y_1=3 \).

Step 2: Substitute into point - slope form

Substitute these values into the formula \( y - y_1=m(x - x_1) \):
\( y - 3=-2(x - (-4)) \)
Simplify the right - hand side:
\( y - 3=-2(x + 4) \)
Expand the right - hand side:
\( y - 3=-2x-8 \)
Add 3 to both sides to get the slope - intercept form (\( y=mx + b \)):
\( y=-2x-8 + 3 \)
\( y=-2x-5 \)

Answer:

If we were finding the equation of the line, the equation is \( y=-2x - 5 \) (in slope - intercept form) or \( y - 3=-2(x + 4) \) (in point - slope form)