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Answer:
The equation of the line in slope-intercept form is:
y = -1/6x + 4
Step-by-step explanation:
The slope-intercept form of the line equation
where
- m is the slope
- b is the y-intercept
Given the points on the line graph
- (0, 4)
- (6, 3)
Determining the slope between (0, 4) and (6, 3)
- (x₁, y₁) = (0, 4)
- (x₂, y₂) = (6, 3)
Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [3 - 4] / [6 - 0]
= -1 / 6
Thus, the slope of the line = m = -1/6
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 = 4
Thus, the y-intercept b = 4
now substituting b = 4 and m = -1/6 in the slope-intercept form
y = mx + b
y = -1/6x + 4
Therefore, the equation of the line in slope-intercept form is:
y = -1/6x + 4