Answer:
See explanations below
Step-by-step explanation:
Slope intercept form of the equation is expressed as y = mx+b
m is the slope
b is the intercept
Given the coordinates (4, -11/3) and (1/2, -29/6)
Slope m = -29/6-(-11/3)÷(1/2-4)
m = (-29/6+11/3)÷(-7/2)
m = -29+22/6÷(-7/2)
m = -7/6÷(-7/2)
m = -7/6×2/-7
m = 2/6
m = 1/3
Get the intercept b
Substitute m= 1/3 and (4, -11/3) into y = MX+b
-11/3 = 1/3(4)+b
-11/3 = 4/3+b
b= -11/3-4/3
b= -15/3
b =-5
Get the required equation
y = 1/3 x -5 (slope-intercept form)
Point slope form of the equation is expressed as y-y0 = m(x-x0)
Substituting m = 1/3 and the point (4,-11/3)
x0 = 4
y0 = -11/3
y - (-11/3) = 1/3(x-4)
y+11/3 = 1/3(x-4) (point-slope form)
For standard format
Recall that y = 1/3x - 5
Multiply through by 3
3y = 1/3x(3)-5(3)
3y = x-15
3y-x = -15(standard form)
