Answer:
[tex]y=3[/tex]
Step-by-step explanation:
The slope of a line is given as [tex]m=\frac{\Delta y}{\Delta x}[/tex], where [tex]\Delta y[/tex] is change in y-value and [tex]\Delta x[/tex] is change in x-value for any two points the line passes through.
Using the points (0, 3) and (4, 3) as given in the problem, we have:
[tex]m=\frac{0}{-4}=0[/tex]. Therefore, the slope of this line is 0.
In slope-intercept form, we have [tex]y=mx+b[/tex]. Since we've found out that [tex]m=0[/tex] the entire term [tex]mx[/tex] will be equal to 0 and we are left with [tex]y=b[/tex], where [tex]b[/tex] is the y-intercept. We can plug in the coordinates of any point the line passes through to find this value:
Using the point (4, 3) as given in the problem:
[tex]3=0(4)+b,\\3=0+b,\\b=3[/tex]
Thus, the equation of our line is [tex]y=0x+3,\\\boxed{y=3}[/tex]
