What is the equation of the following line? (-2,-3) and (0,0)

Answer 1

Two ways to approach.

One is to use the slope intercept form of linear equation

Y=MX+B, where B is the Y intercept (i.e. the value of Y when the line crosses the X axis where X=0)

Since (X,Y)=(0,0), the Y intercept, B, is 0.

So we are now working with Y=MX, and,

dividing both sides by X,

Y/X=M for ALL corresponding values of X and Y, including (X,Y)=(-2,-3)

(-3)/(-2)=M

M=3/2

So, Y=(3/2)X

Another way to approach is using the point slope form of linear equation:

Y-Yo=M(X-Xo),

which is based on the slope being

the change in Y, (Y-Yo),

divided by

the change in X, (X-Xo)

so that M=(Y-Yo)/(X-Xo), and

multiplying both sides by (X-Xo)

So, replacing in

Y-Yo=M(X-Xo)

using the point (-2,-3) and that

M, the change in Y divided by the change in X, or

M=(-3-0)/(-2-0)=-3/-2=3/2

Y-(-3)=(3/2)(X-(-2))

Y+3=(3/2)(X+2)

Y=(3/2)(X+2)-3

Y=(3/2)(X)+(3/2)*2-3

Y=(3/2)(X)+3-3

Y=(3/2)(X)+0

Y=(3/2)X

Answer 2

well the slope is M = (-3 -0)/(-2-0) = -3/-2 = 3/2

also (0,0) is the intercept... see, watch!

B = y - mx = 0 - (3/2)(0) = 0 - 0 = 0

so the equation of the line is y = (3/2)x

note that when x = -2, y = (3/2)(-2) = -3, so (-2,-3) is on the line