y=-3x-3
Explanation
Step 1
find the slope of the line:
when you know 2 points of a line, P1 and P2, the slope is given by:
[tex]\begin{gathered} \text{slope}=\frac{changein\text{ y }}{\text{change in x}}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]
then, pick 2 coordinates of the line and replace
let
P1(0,-3)
P2(-1,0)
replace
[tex]\begin{gathered} \text{slope}=\frac{0-(-3)}{-1-0} \\ \text{slope}=\frac{3}{-1} \\ \text{slope}=-3 \end{gathered}[/tex]
Step 2
find the y-intercept
the y intercept is the y value where the lines intersects the y axis
so, by checkin in the graph we have:
[tex]\begin{gathered} y\text{ intercept=-3} \\ as\text{ ordered pair} \\ (0,-3) \end{gathered}[/tex]
Step 3
find the equation of the line:
a line can be expressed as
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept,this is called, slope intercept point form, then replace
[tex]y=-3x-3[/tex]
so, to check the y intercept, we can do
find y, when x= 0
[tex]\begin{gathered} f(0)=-3(0)-3 \\ f(0)=0-3 \\ f(0)=-3 \\ (0,-3) \end{gathered}[/tex]
I hope this helps you
