Question

x | y
-2 | 10
-4 | 4
-6 | -2
-8 | -8
-10 | -14
-12 | -20
what is the equation of the linear function?
options:
y = 3x + 10
y = 3x + 16
y = -3x + 10
y = -3x + 16

Explanation:

Step1: Calculate slope (m)

Use two points, e.g., $(-2,10)$ and $(-4,4)$:
$$m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-10}{-4-(-2)}=\frac{-6}{-2}=3$$

Step2: Find y-intercept (b)

Substitute $m=3$, $x=-2$, $y=10$ into $y=mx+b$:
$$10=3(-2)+b \implies 10=-6+b \implies b=16$$

Step3: Form linear equation

Combine $m$ and $b$:
$$y=3x+16$$

Answer:

B. $y = 3x + 16$