Question

Find the equation of the line that Passes through (0,-4) and (-4,5)

Answer 1

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;

`y\text{ = mx + c}`

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;

`\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{ = }(5-(-4))/(-4-0)\text{ = }(9)/(-4)\text{ = }(-9)/(4) \end{gathered}`

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;

`y\text{ = }(-9)/(4)x\text{ + c}`

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;

`\begin{gathered} -4\text{ = }(-9)/(4)(0)\text{ + c} \\ \\ -4\text{ = c} \\ \\ \text{Thus the value of c is -4} \end{gathered}`

The complete equation is thus given below as follows;

`\begin{gathered} y\text{ = }(-9)/(4)x\text{ - 4} \\ \\ We\text{ can also multiply through by 4 to get} \\ \\ 4y\text{ = -9x - 16} \end{gathered}`