Write all linear equations in slope-intercept form.
-The amount of time t it takes a flame to go out in a closed container is a linear function of the volume of the container x. A flame in 656 mL container takes 12 seconds to go out and a flame in a
984 mL container takes 20 seconds. Write a linear function that relates t to x.
A) $t = \frac { 4 } { 205 } x - \frac { 4 } { 5 }$
B) $t = \frac { 1 } { 41 } x - 4$
C) $t = 41 x - 4$
D) $t = \frac { 1 } { 41 } x$

Question

Write all linear equations in slope-intercept form.
-The amount of time t it takes a flame to go out in a closed container is a linear function of the volume of the container x. A flame in 656 mL container takes 12 seconds to go out and a flame in a
984 mL container takes 20 seconds. Write a linear function that relates t to x. 
A) $t = \frac { 4 } { 205 } x - \frac { 4 } { 5 }$
B) $t = \frac { 1 } { 41 } x - 4$
C) $t = 41 x - 4$
D) $t = \frac { 1 } { 41 } x$

Quizplus · Accepted Answer

To find the slope $m$ of the linear function, use the two given points $(656, 12)$ and $(984, 20)$. The slope $m = \frac{20 - 12}{984 - 656} = \frac{8}{328} = \frac{1}{41}$. To find the y-intercept $b$, use one of the points and the slope in the equation $y = mx + b$. Using the point $(656, 12)$, $12 = \frac{1}{41} \cdot 656 + b$, solving for $b$ gives $b = 12 - 16 = -4$. Thus, the equation is $t = \frac{1}{41}x - 4$.

Write All Linear Equations in Slope-Intercept Form t=4205x−45t = \frac { 4 } { 205 } x - \frac { 4 } { 5 }t=2054​x−54​

Write All Linear Equations in Slope-Intercept Form $t = \frac { 4 } { 205 } x - \frac { 4 } { 5 }$