Three points are on the same line if the slope of the line through the first two points is the same as the slope of the line through the second two points. For what value of \(c\) are the three points \((2,4)\), \((6,3)\), and \((-5,c)\) on the same line?

tertre Mar 11, 2018

#1**+2 **

Slope = rise/ run or (y1-y2) / (x1-x2)

for the first two points

slope = (4-3) / (2-6) = - 1/4

for the second and third points we need slope = -1/4 , then solve for c

(3-c) / (6-(-5) ) = -1/4

3-c = -1/4(11)

3-c = -11/4

3+11/4 = c

23/4 = c or 5 3/4 or 5.75

ElectricPavlov Mar 11, 2018

#1**+2 **

Best Answer

Slope = rise/ run or (y1-y2) / (x1-x2)

for the first two points

slope = (4-3) / (2-6) = - 1/4

for the second and third points we need slope = -1/4 , then solve for c

(3-c) / (6-(-5) ) = -1/4

3-c = -1/4(11)

3-c = -11/4

3+11/4 = c

23/4 = c or 5 3/4 or 5.75

ElectricPavlov Mar 11, 2018