Write all linear equations in slope-intercept form.
-A biologist recorded 8 snakes on 23 acres in one area and 16 snakes on 37 acres in another area. Find a linear equation that models the number of snakes in x acres.
A) $y = x + 15$
B) $y = \frac { 4 } { 7 } x - \frac { 36 } { 7 }$
C) $y = \frac { 4 } { 7 } x + \frac { 36 } { 7 }$
D) $y = \frac { 7 } { 4 } x - \frac { 7 } { 36 }$

Question

Write all linear equations in slope-intercept form.
-A biologist recorded 8 snakes on 23 acres in one area and 16 snakes on 37 acres in another area. Find a linear equation that models the number of snakes in x acres. 
A) $y = x + 15$
B) $y = \frac { 4 } { 7 } x - \frac { 36 } { 7 }$
C) $y = \frac { 4 } { 7 } x + \frac { 36 } { 7 }$
D) $y = \frac { 7 } { 4 } x - \frac { 7 } { 36 }$

Quizplus · Accepted Answer

To find the linear equation that models the number of snakes in $x$ acres, we first calculate the slope ($m$) using the given points (23, 8) and (37, 16). The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$, which gives us $m = \frac{16 - 8}{37 - 23} = \frac{8}{14} = \frac{4}{7}$. To find the y-intercept ($b$), we use one of the points and the slope in the equation $y = mx + b$. Substituting the point (23, 8) and $m = \frac{4}{7}$, we get $8 = \frac{4}{7} \cdot 23 + b$, solving for $b$ gives $b = -\frac{36}{7}$. Therefore, the equation is $y = \frac{4}{7}x - \frac{36}{7}$.

Write All Linear Equations in Slope-Intercept Form y=x+15y = x + 15y=x+15

Write All Linear Equations in Slope-Intercept Form $y = x + 15$