Respuesta :
The equation of the line that passes through the given points is;
4y = -9x - 16
Here, we are tasked with writing the linear equation of the line that passes through the given points
Mathematically, the linear equation can be represented by;
[tex]y\text{ = mx + c}[/tex]Where m represents the slope of the line while c is the y-intercept of the line. Hence, we want to calculate the values of m and c
To calculate the slope of the line, the equation below is used;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_{2\text{ }}-x_1} \\ \\ (x_{1,\text{ }}y_1)\text{ = (0,-4)} \\ (x_2,y_2)\text{ = (-4,5)} \\ \\ m\text{ = }\frac{5-(-4)}{-4-0}\text{ = }\frac{9}{-4}\text{ = }\frac{-9}{4} \end{gathered}[/tex]Since we have the slope, we can now proceed to get the value of c which is the y-intercept. The value of c can be obtained by plugging the values of the coordinates of one of the points into the yet to be completed equation
In the present form, the equation is;
[tex]y\text{ = }\frac{-9}{4}x\text{ + c}[/tex]We now proceed to plug the coordinates of (0,-4) where x here is 0 and y is -4. Plugging these values into the equation, we have the following;
[tex]\begin{gathered} -4\text{ = }\frac{-9}{4}(0)\text{ + c} \\ \\ -4\text{ = c} \\ \\ \text{Thus the value of c is -4} \end{gathered}[/tex]The complete equation is thus given below as follows;
[tex]\begin{gathered} y\text{ = }\frac{-9}{4}x\text{ - 4} \\ \\ We\text{ can also multiply through by 4 to get} \\ \\ 4y\text{ = -9x - 16} \end{gathered}[/tex]