Complete the equation of the line through (-1,,6)left parenthesis, minus, 1, comma, 6, right parenthesis and (7,-2)(7,? 2)left parenthesis, 7, comma, minus, 2, right parenthesis. use exact numbers. y=y=y, equals

The equation of the line passing through the point s (-1, 6) and (7, -2) is y = -x + 5

The formula for calculating the equation of a line is expressed as y = mx + b where;

m is the slope of the line

b is the y-intercept

Given the coordinate points  (-1,6) and (7, -2)

Get the slope:

Slope = -2-6/7-(-1)

Slope = -8/8

Slope = - 1

Get the y-intercept:

-2 = -1(7) + b

-2 = -7 + b

b = -2 + 7

b = 5

Get the required equation:

Recall that y = mx + b

Substituting m = -1 and b = 5 into the equation:

y = -x + 5

Hence the equation of the line passing through the point s (-1, 6) and (7, -2) is y = -x + 5

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  y = -x +5

Step-by-step explanation:

The 2-point form of the equation of a line is useful for this.

  y = (y2 -y1)/(x2 -x1)(x -x1) + y1 . . . 2-point form of equation for a line

  y = (-2 -6)/(7 -(-1))/(x -(-1)) +6 . . . . substitute the give points

  y = -8/8(x +1) +6 . . . . . . . . . . . . . . simplify a bit; next, simplify more

  y = -x +5

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