Answer:
2. The rate of change in the table is -6
3. The slope of the line is [tex]\frac{3}{2}[/tex] ⇒ d
Step-by-step explanation:
Let us start with no. 2
∵ The rate of change is the constant ration between x and y
∴ The rate of change is the slope of the line represents the table
- The rule of the slope is [tex]m=\frac{y2-y1}{x2-x1}[/tex] , (x1, y1) and (x2, y2) are two points on the line
∵ (1, -3) and (2, -9) are two points on the line
∴ x1 = 1 and y1 = -3
∴ x2 = 2 and y2 = -9
→ Substitute them in the rule of the slope above
∴ [tex]m=\frac{-9-(-3)}{2-1}=\frac{-9+3}{1}=\frac{-6}{1}[/tex]
∴ m = -6
∴ The rate of change in the table is -6
Let us solve no.3
∵ The rule of the slope is [tex]m=\frac{y2-y1}{x2-x1}[/tex] , (x1, y1) and (x2, y2) are two points
on the line
→ Choose from the graph any two points on the line
∵ (0, 0) and (4, 6) are two points on the line
∴ x1 = 0 and y1 = 0
∴ x2 = 4 and y2 = 6
→ Substitute them in the rule of the slope above
∴ [tex]m=\frac{6-0)}{4-0}=\frac{6}{4}=\frac{3}{2}[/tex]
∴ m = [tex]\frac{3}{2}[/tex]
∴ The slope of the line is [tex]\frac{3}{2}[/tex]
