Question

select all of the equations that model the line shown on the graph.
a) $y - 1 = \frac{2}{5}(x - 3)$
b) $y + 1 = \frac{2}{5}(x + 3)$
c) $y - 1 = \frac{2}{5}(x - 2)$
d) $y + 1 = \frac{2}{5}(x + 2)$
e) $y - 1 = \frac{5}{2}(x - 2)$
f) $y + 1 = \frac{5}{2}(x + 3)$

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Using points $(2,1)$ and $(-3,-1)$:
$m=\frac{1-(-1)}{2-(-3)}=\frac{2}{5}$

Step2: Check point-slope form for $(2,1)$

Point-slope form: $y-y_1=m(x-x_1)$. Substitute $m=\frac{2}{5}$, $x_1=2$, $y_1=1$:
$y-1=\frac{2}{5}(x-2)$

Step3: Check point-slope form for $(-3,-1)$

Substitute $m=\frac{2}{5}$, $x_1=-3$, $y_1=-1$ into point-slope form:
$y-(-1)=\frac{2}{5}(x-(-3))$ which simplifies to $y+1=\frac{2}{5}(x+3)$

Answer:

B) $y + 1 = \frac{2}{5}(x + 3)$, C) $y - 1 = \frac{2}{5}(x - 2)$