Respuesta :
[tex]y=\frac{3x}{5}-\frac{1}{5}[/tex]
the line does not pass through the point C(5,3)
Explanation
Step 1
find the equation of the line, to do that,
a) find the slope using:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Let
[tex]\begin{gathered} (x_1,y_1)=A(-3,-2) \\ (x_2,y_2)=B(2,1) \end{gathered}[/tex]hence, the slope is
[tex]\begin{gathered} \text{slope}=\frac{1-(-2)}{2-(-3)} \\ \text{slope}=\frac{3}{5} \end{gathered}[/tex]b) using the slope and the point A find the equation
[tex]\begin{gathered} y-y_0=slope(x-x_0)\text{ Equation slope-point} \\ \text{replace} \\ y-(-2)=\frac{3}{5}(x-(-3)) \\ y+2=\frac{3x}{5}+\frac{9}{5} \\ y=\frac{3x}{5}+\frac{9}{5}-2 \\ y=\frac{3x}{5}-\frac{1}{5} \end{gathered}[/tex]Step 2
Does it also pass through the point C(5,3)?
to answer this you have to replace the values for x and y and check if it is true
Let
C(5,3) x=5 y=3
[tex]\begin{gathered} y=\frac{3x}{5}-\frac{1}{5} \\ 3=\frac{3(5)}{5}-\frac{1}{5} \\ 3=\frac{15}{5}-\frac{1}{5} \\ 3=\frac{14}{5\text{ }}\text{ False} \\ \text{then} \end{gathered}[/tex]the line does not pass through the point C(5,3)
