Answer:
The slope of the line is: [tex]m=-\frac{1}{2}[/tex]
The y-intercept b = 3
The slope-intercept equation of the line is: [tex]y\:=\:-\frac{1}{3}x+3[/tex]
Step-by-step explanation:
Taking two points from the given graph
(0, 3) and (6, 0)
Determining the slope m
The slope between (0, 3) and (6, 0) using the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where m is the slope between (x₁, y₁) and (x₂, y₂)
In our case,
now substitute (x₁, y₁) = (0, 3) and (x₂, y₂) = (6, 0) in the slope formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{0-3}{6-0}[/tex]
[tex]m=-\frac{3}{6}[/tex]
[tex]m=-\frac{1}{2}[/tex]
Thus, the slope of the line is: [tex]m=-\frac{1}{2}[/tex]
Determining the y-intercept (b)
The slope-intercept form of the line equation is given by
[tex]y = mx+b[/tex]
where
- [tex]m[/tex] is the slope
- [tex]b[/tex] is the y-intercept
From the graph, we can figure out the y-intercept by checking the value of y at x = 0.
If we closely check the graph, at x = 0, the value of y = 3
Therefore, the y-intercept b = 3
Slope-intercept Equation
We already know that the slope-intercept form of the line equation is
[tex]y = mx+b[/tex]
substituting b = 3 and m = -1/2
[tex]y\:=\:-\frac{1}{2}x+3[/tex]
Therefore, the slope-intercept equation of the line is: [tex]y\:=\:-\frac{1}{2}x+3[/tex]
The graph is also attached below.
