SAT Question af711d1b: Linear Functions answer and explanation with Desmos solution

Choice C is correct. The average time $t$, in minutes, it takes Carly to travel a certain distance $d$, in kilometers, is given in the table. This linear relationship can be represented by an equation in the form $t=ad+b$, where $a$ and $b$ are constants. The table shows that it takes Carly an average time of $8$ minutes to travel $0.32$ kilometers. Substituting $8$ for $t$ and $0.32$ for $d$ in the equation $t=ad+b$ yields $8=0.32a+b$. Subtracting $0.32a$ from both sides of this equation yields $8-0.32a=b$. The table also shows that it takes Carly an average time of $14$ minutes to travel $0.56$ kilometers. Substituting $14$ for $t$ and $0.56$ for $d$ in the equation $t=ad+b$ yields $14=0.56a+b$. Subtracting $0.56a$ from both sides of this equation yields $14-0.56a=b$. Substituting $8-0.32a$ for $b$ in this equation yields $14-0.56a=8-0.32a$. Subtracting $8$ from both sides of this equation yields $6-0.56a=-0.32a$. Adding $0.56a$ to both sides of this equation yields $6=0.24a$. Dividing both sides of this equation by $0.24$ yields $25=a$. Substituting $25$ for $a$ in the equation $8=0.32a+b$ yields $8=0.32(25)+b$, or $8=8+b$. Subtracting $8$ from both sides of this equation yields $0=b$. Substituting $25$ for $a$ and $0$ for $b$ in the equation $t=ad+b$ yields $t=25d+0$, or $t=25d$.