Question

In the coordinate plane above, there is a circle with center at point (4.3). Two points that lie on the cirde are A(1.-1) and B(86). a. Determine the equation of the line that goes through points A and B

Answer 1

Given the coordinates of the points of a line on the circle A(1.-1) and B(8, 6). To get the equation of the line, we will need to get the slope and the intercept of the line.

The standarad equation of a line is expressed as y = mx+c

m is the slope

c is the intercept

m = y2-y1/x2-x1

Substitute the coordnate points into the formula;

m = 6-(-1)/8-1

m = 6+1/7

m = 7/7

m = 1

Next is to get the intercept of the line. You can do this ny substituting m = 1 any of the points into the equation ofa line and calculate c as shown

y = mx+c

Using point (1, -1)

-1 = 1(1)+c

-1 = 1 + c

c = -1-1

c = -2

Substitute m =1 and c = -2 into the formula to the required equation as shown;

y = 1x+ (-2)

y = x - 2

Hence the equation of the line that goes through points A and B​ is y = x-2