Question

the graph of a linear function passes through (-8,-4) and (4, 5) what is the equation of the function?
a ( y = -\frac{3}{4}x + 2 )
b ( y = \frac{3}{4}x + 2 )
c ( y = -\frac{4}{3}x + 6 )
d ( y = \frac{4}{3}x + 6 )

Explanation:

Step1: Calculate the slope

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2-y_1}{x_2-x_1}$. Using $(-8,-4)$ and $(4,5)$:
$m=\frac{5-(-4)}{4-(-8)}=\frac{9}{12}=\frac{3}{4}$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=\frac{3}{4}$ and point $(4,5)$:
$5=\frac{3}{4}(4)+b$
$5=3+b$
$b=5-3=2$

Step3: Form the equation

Substitute $m=\frac{3}{4}$ and $b=2$ into $y=mx+b$:
$y=\frac{3}{4}x+2$

Answer:

B. $y=\frac{3}{4}x+2$