Solve the problem. Write all linear equations in slope-intercept form.
-A biologist recorded 2 snakes on 14 acres in one area and 20 snakes on 31 acres in another area. Find a linear equation that models the number of snakes in $\mathrm { x }$ acres.
A) $y = \frac { 18 } { 17 } x + \frac { 218 } { 17 }$
B) $y = x + 12$
C) $y = \frac { 18 } { 17 } x - \frac { 218 } { 17 }$
D) $y = \frac { 17 } { 18 } x - \frac { 17 } { 218 }$

Question

Quizplus · Accepted Answer

To find the linear equation that models the number of snakes in $x$ acres, we use the two points given: (14, 2) and (31, 20). The slope $m$ of the line is calculated as $\frac{20 - 2}{31 - 14} = \frac{18}{17}$. To find the y-intercept $b$, we can use one of the points and the slope in the equation $y = mx + b$. Using the point (14, 2), we get $2 = \frac{18}{17} \cdot 14 + b$, solving for $b$ gives $b = -\frac{218}{17}$. Thus, the equation is $y = \frac{18}{17}x - \frac{218}{17}$.

Solve the Problem x\mathrm { x }x Acres A) y=1817x+21817y = \frac { 18 } { 17 } x + \frac { 218 } { 17 }y=1718​x+17218​

Solve the Problem $\mathrm { x }$ Acres
A) $y = \frac { 18 } { 17 } x + \frac { 218 } { 17 }$