Question

write an equation in slope-intercept form of the line that passes through the gi\

x	y	\
-4	9	\
-2	4	\
2	-6	\
4	-11

Explanation:

Step1: Calculate the slope

Use two points \((x_1,y_1)=(-4,9)\) and \((x_2,y_2)=(-2,4)\). The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

$$ m=\frac{4 - 9}{-2 - (-4)}=\frac{-5}{2}=-\frac{5}{2} $$

Step2: Find the y - intercept

Use the slope - intercept form \(y = mx + b\) and the point \((-4,9)\). Substitute \(x=-4\), \(y = 9\) and \(m=-\frac{5}{2}\) into the equation:

$$ 9=-\frac{5}{2}(-4)+b $$

$$ 9 = 10 + b $$

Subtract 10 from both sides: \(b=9 - 10=-1\)

Step3: Write the equation

The slope - intercept form is \(y=mx + b\). Substitute \(m = -\frac{5}{2}\) and \(b=-1\) into the formula:

$$ y=-\frac{5}{2}x-1 $$

Answer:

\(y = -\frac{5}{2}x-1\)