Question

Find an equation for the passes through the point (1,-4) and (-5,-2)

Answer 1

`y=-(x)/(3)-(11)/(3)`

Step-by-step explanation:

The point-slope form of the equation of a line is given as;

`y-y_1=m(x-x_1)`

where m = the slope of the line

x1 and y1 = coordinates of a point on the line

Given the coordinates (1,-4) and (-5,-2)​, let's go ahead and determine the slope of the line where x1 = 1, y1 = -4, x2 = -5 and y2 = -2;

`m=(y_2-y_1)/(x_2-x_1)=(-2-(-4))/(-5-1)=(-2+4)/(-6)=-(2)/(6)=-(1)/(3)`

Since our m = -1/3, let's go ahead and write the required equation using the point (1, -4) where x1 = 1 and y1 = -4;

`\begin{gathered} y-(-4)=-(1)/(3)(x-1) \\ y+4=-(x)/(3)+(1)/(3) \\ y=-(x)/(3)+(1)/(3)-4 \\ y=-(x)/(3)-(11)/(3) \end{gathered}`