Question

determine the equation of the line that passes through the given points. (if you have a graphing calculator, you can use the table feature to confirm that the coordinates of both points satisfy your equation.)(3.5, 8.2) and (2, 7.3)a. $y = -0.6x - 6.1$b. $y = 0.6x - 6.1$c. $y = -0.6x + 6.1$d. $y = 0.6x + 6.1$please select the best answer from the choices provideda\
b\
c\
d

Explanation:

Step1: Calculate the slope (m)

The formula for slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Given points $(3.5, 8.2)$ and $(2, 7.3)$, so $x_1 = 3.5$, $y_1 = 8.2$, $x_2 = 2$, $y_2 = 7.3$.
$m=\frac{7.3 - 8.2}{2 - 3.5}=\frac{-0.9}{-1.5}=0.6$.

Step2: Use point - slope form to find the equation

The point - slope form is $y - y_1=m(x - x_1)$. Let's use the point $(2, 7.3)$ and $m = 0.6$.
$y - 7.3=0.6(x - 2)$
Expand the right - hand side: $y - 7.3 = 0.6x-1.2$
Add 7.3 to both sides: $y=0.6x-1.2 + 7.3$
Simplify: $y = 0.6x+6.1$

We can also check by plugging the points into the equation.
For the point $(3.5,8.2)$:
Left - hand side (LHS)=$8.2$
Right - hand side (RHS)=$0.6\times3.5 + 6.1=2.1+6.1 = 8.2$. LHS = RHS.
For the point $(2,7.3)$:
LHS=$7.3$
RHS=$0.6\times2+6.1 = 1.2 + 6.1=7.3$. LHS = RHS.

Answer:

d. $y = 0.6x + 6.1$