Write all linear equations in slope-intercept form.
-A company can make 9 satellite dishes for $92,300, while 16 satellite dishes cost $97,130. Find a linear equation that models the cost to produce x satellite dishes.
A) $y = 7 x + 4830$
B) $y = 690 x + 86,090$
C) $y = 690 x - 86,090$
D) $y = x + 4830$

Question

Write all linear equations in slope-intercept form.
-A company can make 9 satellite dishes for $92,300, while 16 satellite dishes cost $97,130. Find a linear equation that models the cost to produce x satellite dishes. 
A) $y = 7 x + 4830$
B) $y = 690 x + 86,090$
C) $y = 690 x - 86,090$
D) $y = x + 4830$

Quizplus · Accepted Answer

To find the slope ($m$) of the line, we use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line. Substituting the given points (9, 92300) and (16, 97130), we get $m = \frac{97130 - 92300}{16 - 9} = \frac{4830}{7} = 690$. To find the y-intercept ($b$), we use one of the points and the slope in the equation $y = mx + b$. Substituting $x = 9$, $y = 92300$, and $m = 690$ gives $92300 = 690(9) + b$, solving for $b$ gives $b = 86090$. Therefore, the equation is $y = 690x + 86090$.

Write All Linear Equations in Slope-Intercept Form y=7x+4830y = 7 x + 4830y=7x+4830

Write All Linear Equations in Slope-Intercept Form $y = 7 x + 4830$