Answer:
[tex]y=\frac{-1}{2}x+7[/tex]
Step-by-step explanation:
Slope intercept form: [tex]y=mx+b[/tex] when [tex]m[/tex] is the slope of the line and [tex]b[/tex] is the y-intercept (the y-coordinate of the point the line crosses the y-axis)
1) Find the slope ([tex]m[/tex])
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] when the points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
We can use any two points that the table gives us to plug into this equation. For example, we can use the points (14,0) and (0,7):
[tex]m=\frac{0-7}{14-0}\\m=\frac{-7}{14}[/tex]
Simplify the fraction
[tex]m=\frac{-1}{2}[/tex]
So far, our equation looks like this:
[tex]y=\frac{-1}{2}x+b[/tex]
2) Find the y-intercept ([tex]b[/tex])
The y-intercept is the y-coordinate of the point the line crosses the y-axis, or in other words, it's the value of y when x is equal to 0.
Looking at the table, we can see that y is equal to 7 when x is equal to 0, so, therefore, [tex]b=7[/tex].
Now, this is our final equation after plugging in [tex]m[/tex] and [tex]b[/tex]:
[tex]y=\frac{-1}{2}x+7[/tex]
I hope this helps!
