Question

Question 2

write the equation of ABin slope-intercept form. Then check whether Clies on AB by substituting the coordinates of point Cinto the equation.
Show your work

Answer 1

the equation of A⁢B↔ is y = 0.5x + 0.5.

Explanation:

Answers will vary based on the method used, but the final slope-intercept form of the equation of A⁢B↔ will be the same.

Let the equation of A⁢B↔ in slope-intercept form be y=m⁢x+d, where m is the slope and d is the y-intercept.

The coordinates of points A and B are (1, 1) and (5, 3), respectively, so the slope of A⁢B↔ is

m=yB−yA/xB−xA=24=0.5.

Substitute the value of m back in the equation:

y = 0.5x + d.

Substitute the coordinate of point A (1, 1) in the equation above, and solve for d:

1 = 0.5 + d

d = 0.5.

Therefore, the equation of A⁢B↔ is y = 0.5x + 0.5.

To check whether C lies on A⁢B↔ substitute the x-coordinate of C into the right side of the equation: 0.5 (2.6) + 0.5 = 1.8.

The result is equal to the y-coordinate of C. Thus, C satisfies the equation of A⁢B↔ which means that C lies on A⁢B↔.