Answer:
The equation of the line in slope-intercept form is:
[tex]y = x + 4[/tex]
Step-by-step explanation:
The slope-intercept form of the line equation
y = mx+b
where m is the slope and b is the y-intercept
Given the equation
Determining the slope between (1, 5) and (2, 6)
(x₁, y₁) = (1, 5)
(x₂, y₂) = (2, 6)
Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [5 - 4] / [1 - 0]
= 1 / 1
= 1
Thus, the slope of the line = m = 1
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 in the slope-intercept form
[tex]y = mx + b[/tex]
[tex]y = (1)x + 4[/tex]
[tex]y = x + 4[/tex]
Therefore, the equation of the line in slope-intercept form is:
[tex]y = x + 4[/tex]
