The equation of a line takes the general form y = mx + c where
m = gradient
c = intercept on the y axis
Every point is represented by coordinates, i.e, where they occur on the x and y axis in the form (x,y)
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}=\text{ }\frac{9-1}{2-4}=\text{ }\frac{8}{-2}=\text{ -4}[/tex]
Getting the y intercept and the equation of the line will require us to use the below formula:
[tex]\begin{gathered} \text{ }\frac{y_{}-y_{_1}}{x_{}-x_1}=\text{ }\frac{y_2-y_1}{x_2-x_1}\text{ where }\frac{y_2-y_1}{x_2-x_1}=-4 \\ \frac{y-1}{x-4}=-4,\text{ Crossmultiplying, we have:} \\ 4x-4(-4)\text{ = }y-1 \\ 4x+16\text{ = }y-1\text{ Adding 1 to both sides give} \\ 4x+16\text{ + 1 = y} \\ y\text{ = 4x }+17 \end{gathered}[/tex]
Therefore, the intercept on y axis is 17 and gradient is -4
