PART a)
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
From the figure, let us take two points
Finding the slope between (0, 3) and (-1, 6)
(x₁, y₁) = (0, 3)
(x₂, y₂) = (-1, 6)
Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [6 - 3] / [-1 - 0]
= 3 / -1
= -3
Thus, the slope of the line = m = -3
We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
From the graph, it is clear
at x = 0, y = 3
Thus, the y-intercept b = 3
Now, substituting b = 3 and m = -3 in slope-intercept form of the line equation
[tex]y = mx+b[/tex]
y = -3x+3
Therefore, the rule for the graph 'a' is:
y = -3x+3
PART b)
Given
- The slope = rise / run = 4/1
From the graph, it is clear that:
The slope m = [y₂ - y₁] / [x₂ - x₁]
= +4 / +1
= 4/1
= 4
We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
From the graph, it is clear
at x = 0, y = 10
Thus, the y-intercept b = 10
now substituting m = 4 and b = 10 in slope-intercept form of the line equation
[tex]y = mx+b[/tex]
y = 4x+10
Therefore, the rule for the graph 'a' is:
y = 4x+10
