Question

Find the equation of the line with the given properties. Passes through (4, -5) with a slope of -1\2

Answer 1

$y=-\frac{1}{2}x-3$

Explanation

when you know the slope and a passing point of the line, you can find the equation of the line by replacing in the slope-point equation ,it is given by:

$\begin{gathered} y-y_1=m(x-x_1) \\ \text{where } \\ m\text{ is the slope} \\ \text{and} \\ (x_1,y_1)\text{ is a point from the line } \end{gathered}$

then

Step 1

a)Let

$\begin{gathered} \text{slope}=-\frac{1}{2} \\ \text{ Point=(4,-5)} \end{gathered}$

now,replace and solve for y

$\begin{gathered} y-y_1=m(x-x_1) \\ y-(-5)=-\frac{1}{2}(x-4) \\ y+5=-\frac{1}{2}x+\frac{4}{2} \\ y+5=-\frac{1}{2}x+2 \\ \text{subtract 5 in both sides} \\ y+5-5=-\frac{1}{2}x+2-5 \\ y=-\frac{1}{2}x-3 \end{gathered}$

therefore, the answer is

$y=-\frac{1}{2}x-3$

I hope this helps you