Explanation:
The initial value of a linear relationship is the y-intercept. That is, the y-values at which [tex]x=0[/tex]. Here we know that a line passes through the y-axis at -2 and the x-axis at 3. So the initial value is:
[tex]y=-2[/tex]
In order to graph this linear function, let's find its equation. The line passes through these two points:
[tex](0,-2) \ and \ (3,0) \\ \\ Finding \ slope: \\ \\ m=\frac{0-(-2)}{3-0} \\ \\ m=\frac{2}{3} \\ \\ \\ \text{The slope intercept form is found as:} \\ \\ y=mx+b \\ \\ But: \\ \\ m=2/3 \\ \\ b=-2 \\ \\ \\ Then: \\ \\ y=\frac{2}{3}x-2[/tex]
Finally, the graph is shown below and you can see that [tex]y=-2[/tex] is the initial value.
