Question

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

Answer 1

Answer:

The equation of the line is;

$y=-\frac{1}{3}x-3$

Explanation:

Given that;

The line has the same slope as ;

$y=-\frac{1}{3}x+4$

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

$y=mx+b$

The slope m of the line is;

$m=-\frac{1}{3}$

Given that the line passes through point;

$(6,-5)$

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

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

Therefore, the equation of the line is;

$y=-\frac{1}{3}x-3$