Question

Find the equation of the line passingthrough the points (4, 1) and (2,9).y = [? ]x + [ ]yes

Answer 1

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)

`m\text{ = }(y_2-y_1)/(x_2-x_1)=\text{ }(9-1)/(2-4)=\text{ }(8)/(-2)=\text{ -4}`

Getting the y intercept and the equation of the line will require us to use the below formula:

`\begin{gathered} \text{ }\frac{y_{}-y_(_1)}{x_{}-x_1}=\text{ }(y_2-y_1)/(x_2-x_1)\text{ where }(y_2-y_1)/(x_2-x_1)=-4 \\ (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}`

Therefore, the intercept on y axis is 17 and gradient is -4