Question

i. ______ $y = 0.75x + 2$
ii. ______ $y = 0.75(2)^x$
iii. ______ $y = -0.75x - 2$
iv. ______ $y = 2(0.75)^x$
(a)
(b)
(c)
(d)

Explanation:

Step1: Analyze linear equation i

The equation $y=0.75x+2$ is linear with positive slope ($0.75$) and y-intercept $2$. Graph (a) has a positive slope and crosses the y-axis above 0, matching this.

Step2: Analyze exponential equation ii

The equation $y=0.75(2)^x$ is an exponential growth function ($2>1$). When $x=0$, $y=0.75(2)^0=0.75$, so it passes near $(0,0.75)$ and increases as $x$ increases. Graph (b) matches this growth curve.

Step3: Analyze linear equation iii

The equation $y=-0.75x-2$ is linear with negative slope ($-0.75$) and y-intercept $-2$. Graph (c) has a negative slope and crosses the y-axis below 0, matching this.

Step4: Analyze exponential equation iv

The equation $y=2(0.75)^x$ is an exponential decay function ($0<0.75<1$). When $x=0$, $y=2(0.75)^0=2$, so it passes through $(0,2)$ and decreases as $x$ increases. Graph (d) matches this decay curve.

Answer:

i. (a) $y = 0.75x + 2$
ii. (b) $y = 0.75(2)^x$
iii. (c) $y = -0.75x - 2$
iv. (d) $y = 2(0.75)^x$