Question

Write the equation for the line that has the same slope as y = -1/3x + 4 and passes through (6,-5).

Answer 1

The equation of the line is;

`y=-(1)/(3)x-3`

Step-by-step explanation:

Given that;

The line has the same slope as ;

`y=-(1)/(3)x+4`

Compare to the standard slope intercept equation of a straight line;

`y=mx+b`

The slope m of the line is;

`m=-(1)/(3)`

Given that the line passes through point;

`(6,-5)`

let us derive its equation by using the point slope equation of line;

`\begin{gathered} y-y_1=m(x-x_1)_{} \\ \text{substituting the slope and the given point, we have;} \\ y-(-5)=-(1)/(3)(x-6) \\ y+5=-(1)/(3)x+(6)/(3) \\ y+5=-(1)/(3)x+2 \\ y=-(1)/(3)x+2-5 \\ y=-(1)/(3)x-3 \end{gathered}`

Therefore, the equation of the line is;

`y=-(1)/(3)x-3`