Answer:
a. The slope is incorrect
b. y = 3x, ( 0 , 0 )
c) y = 4 - x
Step-by-step explanation:
Given:-
The slope between two points (1, 3) and (6, -2) is 3.
a. Explain why the information Mary was given cannot be correct.
- The slope between two arbitrary points, ( x1 , y1 ) and (x2 , y2) is given by the following relationship:
slope = ( y2 - y1 ) / ( x2 - x1)
- Use the given points (1, 3) and (6, -2) and determine the slope:
slope = ( -2 - 3 ) / ( 6 - 1 )
slope = ( -5 ) / ( 5 )
slope = -1
- Yes, the given slope is incorrect it should be = -1
b.If the given point (1, 3) and the given slope are correct, what is the equation for the line? Give the coordinates of another point on the line
- We will assume the point (1,3) lies on line with a slope = 3.
- We will use the slope-intercept equation of line:
y = slope*x + c
Where, m : Slope
c : y-intercept
y = 3x + c
Using the given correct point to evaluate the y-intercept (c):
3 = 3*1 + c
c = 0
- The equation of line is,
y = 3x
- The origin (0,0) lies on the line y = 3x.
c. If the given points are correct for the line, what is the slope? Write an equation for the line
- We will assume the points (1, 3) and (6, -2) lies on line with a slope calculated in part (a) to be = -1.
- We will use the slope-intercept equation of line:
y = slope*x + c
Where, m : Slope
c : y-intercept
y = -x + c
Using the given points to evaluate the y-intercept (c):
3 = -1 + c
c = 4
- The equation of line is,
y = -x + 4
