y = -21/2 x + 5 (option C)
Explanation:
The points: (-4, 47) and (2, -16)
Using the slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} x_1=-4,y_1=47,x_2=2,y_2\text{ = -1}6 \\ \text{slope = m =}\frac{-16-47}{2-(-4)} \end{gathered}[/tex][tex]\begin{gathered} \text{slope =}\frac{-63}{2+4}=-\frac{63}{6} \\ \text{slope = -21/2} \end{gathered}[/tex]
Equation of line in slope intercept form:
y = mx + b
b =y - intercept. To get b, we would use any of the given point and the slope
using (-4, 47) = (x, y)
47 = -21/2 (-4) + b
47 = 84/2 + b
47 = 42 + b
b = 47 - 42
b = 5
The equation in slope intercept form becomes:
y = -21/2 x + 5 (option C)
