Answer:
y = 2x + 1 ;
y - 3 = - 3(x - 1) ; y = - 3x + 6 ;
Step-by-step explanation:
Given the data:
Sidewalk 1:
x __ y
2 _ 5
0 _ 1
Sidewalk 2:
x __ y
1 _ 3
3 _ -3
Equation for sidewalk 1 in slope - intercept form:
Slope intercept form:
y = mx + c
c = intercept ; m = slope
m = (change in y / change in x)
m = (1 - 5) / (0 - 2) = - 4 / - 2 = 2
Y intercept ; value of y when x = 0
(0, 1) ; y = 1
Hence, c = 1
y = 2x + 1
Sidewalk 2:
Point slope form:
y - y1 = m(x - x1)
m = slope
m = = (-3 - 3) / (3 - 1) = - 6/2 = - 3
Point (x1, y1) = (1, 3)
y - 3 = - 3(x - 1)
To slope intercept form:
y - 3 = - 3(x - 1)
y - 3 = - 3x + 3
y = - 3x + 3 + 3
y = - 3x + 6
Since the slope of both lines are different, intersection will be at single point and will have a single solution. This makes it independent.
Using substitution method :
y = 2x + 1 - - - (1)
y = - 3x + 6 - - - (2)
Substitute (1) into (2)
2x + 1 = - 3x + 6
2x + 3x = 6 - 1
5x = 5
x = 1
From (1)
y = 2(1) + 1
y = 2 + 1
y = 3
Coordinate of the point of intersection = (1, 3)
