Question

1. writing and graphing equations using function notation (graph - 6 points; features 14 points)

the function g is linear. you are given:
g(-2)=7 and g(2)=1
ordered pair 1: ( )
ordered pair 2: ( )
slope (m):
parallel slope:
perpendicular slope:
y - intercept (b):
point - slope equation:

Explanation:

Step1: Find the slope

The two - point formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given the points $(-2,7)$ and $(2,1)$, we have $x_1=-2,y_1 = 7,x_2=2,y_2 = 1$. Then $m=\frac{1 - 7}{2-(-2)}=\frac{-6}{4}=-\frac{3}{2}$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(2,1)$ and $m =-\frac{3}{2}$. So $y - 1=-\frac{3}{2}(x - 2)$. Expand it: $y-1=-\frac{3}{2}x + 3$. Then $y=-\frac{3}{2}x+4$, and the y - intercept $b = 4$.

Step3: Determine parallel and perpendicular slopes

Parallel lines have the same slope. So the parallel slope is $-\frac{3}{2}$. Perpendicular lines have slopes that are negative reciprocals. So the perpendicular slope is $\frac{2}{3}$.

Step4: Write the point - slope equation

Using the point - slope form $y - y_1=m(x - x_1)$ with $m =-\frac{3}{2}$ and the point $(2,1)$, the point - slope equation is $y - 1=-\frac{3}{2}(x - 2)$.

Answer:

Ordered Pair 1: $(-2,7)$
Ordered Pair 2: $(2,1)$
Slope (m): $-\frac{3}{2}$
Y - intercept (b): $4$
Parallel slope: $-\frac{3}{2}$
Perpendicular slope: $\frac{2}{3}$
Point - Slope Equation: $y - 1=-\frac{3}{2}(x - 2)$