Answer:
[tex]y=-\frac{3}{2} x+6[/tex]
Step-by-step explanation:
We need the equation of the line in the form:
[tex]y=mx+b[/tex]
where m is the slope of the line and b is the y-intercept.
y-intercept: the point where the line touches the y axis.
In this case that point is 6. So b = 6
Slope:
is the rate of change between the y-coordinate and the x-coordinate on the graph of the line.
To find the slope we need two points where the line crosses, I will take the points:
[tex](0,6)[/tex] and [tex](2,3)[/tex]
where we name the coordinates as follows:
[tex]x_{1}=0\\y_{1}=6\\x_{2}=2\\y_{2}=3[/tex]
and use the slope equation:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
substituting our values:
[tex]m=\frac{3-6}{2-0}\\ \\m=-\frac{3}{2}[/tex]
and so, gathering the information we find we can define the equation of the line:
[tex]y=mx+b\\\\y=-\frac{3}{2} x+6[/tex]
