Question

Find the equation of the line that passes through the points (-800, 200) and (-400, 300)

Answer 1

The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula

d = √  ((X2-X1)2+(Y2-Y1)2)

d = √ (-400--800)2+(300-200)2

d = √ ((400)2+(100)2)

d = √ (160000+10000)

d = √ 170000

The distance between the points is 412.310562561766

The midpoint of two points is given by the formula

Midpoint= ((X1+X2)/2,(Y1+Y2)/2)

Find the x value of the midpoint

Xm=(X1+X2)/2

Xm=(-800+-400)/2=-600

Find the Y value of the midpoint

Ym=(Y1+Y2)/2

Ym=(200+300)/2=250

The midpoint is: (-600,250)

Graphing the two points, midpoint and distance

P1 (-800,200)

P2 (-400,300)

Midpoint (-600,250)

The length of the black line is the distance between the points (412.310562561766)

Answer 2

Hey there!

First, we need to find the slope. To do this, we subtract the y values and then divide this by the difference in the x values.

300-200/-400+800

100/400

1/4

Our slope is 1/4. Now we plug a point into the slope intercept equation and solve for b.

200=-800(1/4)+b

200=-200+b

b=400

Now, we have our equation.

y=1/4x+400

I hope this helps!