Question

Write the equation of the line through the points (3,2) and (-6,1).

Answer 1

Finding the distance, midpoint, slope, equation and the x y-interceptsof a line passing between the two points p1 (3,2) and p2 (-6,1)The distance (d) between two points (x1,y1) and (x2,y2) is given by the formulad = √ ((X2-X1)2+(Y2-Y1)2)d = √(-6-3)2+(1-2)2d = √((-9)2+(-1)2)
d = √(81+1)
d = √82

The distance between the points is 9.05538513813742

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=(3+-6)/2=-1.5

Find the Y value of the midpoint

Ym=(Y1+Y2)/2
Ym=(2+1)/2=1.5

The midpoint is: (-1.5,1.5)

Graphing the two points, midpoint and distanceP1 (3,2)P2 (-6,1)Midpoint (-1.5,1.5)The length of the black line is the distance between the points (9.05538513813742)
Find the slope of the line connecting the two pointsSlope = (Y2-Y1) = (1-2) = (-1) = 0.111111111111111(X2-X1)(-6-3)(-9)Find the equation of the line passing through the two pointsThe general equation for a straight line isy = mx + bWhere m represents the slope of the line which we found in the previous step to be 0.111111111111111y = 0.11x + bWe substitute x and y for the values from one of our points (3,2)2 = .11×3 + b2 = 0.33 + b2-0.33 = b1.67 = bKnowing both b and m, we can contruct the equation of the liney= 0.11x+ 1.67X and Y interceptsThe x-intercept is a point on the graph where y is zero

Using the equation we found in the previous step and substituting zero for y
y= 0.11x+ 1.670= 0.11x+ 1.67-0.11x= 1.67x= 1.67/-0.11 = -15.00The x intercept for this straight line is -15.00

The y-intercept is a point on the graph where x is zero

Using the equation we found in the previous step and substituting zero for x
y= 0.11×0+ 1.67y= 1.67The y intercept for this straight line is 1.67