What is an equation of the line that passes through the points (6, 2) and (7,1)?

Answer 1

(6,2) and (7,1) have a line through them with an equation that is

(2-1)/(6-7) = (y-2)/(x-6)

1/-1 = -1 = (y-2)/(x-6)

y-2 = -(x-6) = -x +6

y = -x +6 +2

y = -x +8

check the answer, plug in the points

2 =-6+8

1 =-7+8

also plot the points on a graph and

see if the slope makes sense

slope is negative one, downward sloping at a -45 degree angle

the line intercepts/intersects the y axis at (0,8)

x intercept is (8,0)

plot the 2 intercepts and connect them with a straight line. see if the two given points

(6,2) and (7,1) are on that line.

If you want to make sure you didn't make a mistake

slope = "rise over run" = change in y coordinates divided by change in x coordinates

in slope intercept form, the equation is y = slope times x, plus the y intercept

slope = the coefficient of the x term. y intercept is the constant term, when the linear equation is solved for y

y=-x +8 is the equation in slope intercept form

x+y = 8 is the equation in standard form

x+y-8 =0 is the equation in general form

in point slope form, you have two or more choices, depending on which point you use

caveat: all the above assumes the line is a straight line. IF the line is curved, there are an infinite number of equations that could fit going through those two points.