Answer:
[tex]y=-\frac{1}{2}x+3[/tex]
The graph in the attached figure
Step-by-step explanation:
step 1
Find the slope
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
(0,3) and (6,0)
substitute the values in the formula
[tex]m=\frac{0-3}{6-0}[/tex]
[tex]m=\frac{-3}{6}[/tex]
[tex]m=-\frac{1}{2}[/tex]
step 2
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-\frac{1}{2}[/tex]
[tex]b=3[/tex] ----> the y-intercept is given
substitute the values
[tex]y=-\frac{1}{2}x+3[/tex]
step 3
To graph the line plot the intercepts and join the points
The graph in the attached figure
