Question

23
m = -\frac{9}{4}
(-4, 4)

Explanation:

Step1: Identify the problem type

We have a slope \( m = -\frac{9}{4} \) and a point \( (-4, 4) \). We likely need to find the equation of a line using the point - slope form. The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1) \) is a point on the line and \( m \) is the slope.

Step2: Substitute the values into the point - slope formula

Here, \( x_1=-4 \), \( y_1 = 4 \) and \( m=-\frac{9}{4} \). Substituting these values into \( y - y_1=m(x - x_1) \), we get:
\( y - 4=-\frac{9}{4}(x - (-4)) \)
Simplify the right - hand side: \( y - 4=-\frac{9}{4}(x + 4) \)

Step3: Distribute the slope

\( y - 4=-\frac{9}{4}x-9 \)

Step4: Solve for y (to get the slope - intercept form \( y=mx + b \))

Add 4 to both sides of the equation:
\( y=-\frac{9}{4}x-9 + 4 \)
\( y=-\frac{9}{4}x-5 \)

Answer:

If we were finding the equation of the line, the slope - intercept form is \( y =-\frac{9}{4}x-5 \) and the point - slope form is \( y - 4=-\frac{9}{4}(x + 4) \)