Respuesta :
The equation of the line through the given points is;
[tex]3y\text{ = -8x + 28}[/tex]Here, we want to get the equation of the line that passes through the given points
Generally, we have the equation of a line as;
[tex]y\text{ = mx + b}[/tex]where m represents the slope and b represents the y-intercept
To find the slope, we use the slope formula which is as follows;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ (x_1,y_1)\text{ = (2,4)} \\ (x_2,y_2)\text{ = (5,-4)} \\ \\ m\text{ = }\frac{-4-4}{5-2}\text{ = }\frac{-8}{3} \end{gathered}[/tex]Partially, we have the complete equation as;
[tex]y\text{ = }\frac{-8}{3}x\text{ + b}[/tex]To get b, we use any of the points
Let us use the first point
[tex]\begin{gathered} 4\text{ = }\frac{-8}{3}(2)\text{ + b} \\ 4\text{ = }\frac{-16}{3}+\text{ b} \\ \\ b\text{ = 4 + }\frac{16}{3}\text{ = }\frac{12+16}{3}\text{ = }\frac{28}{3} \end{gathered}[/tex]So, the equation of the line is;
[tex]y\text{ = }\frac{-8}{3}x\text{ + }\frac{28}{3}[/tex]Multiply through by 3, we have;
[tex]3y\text{ = -8x + 28}[/tex]