We are told that the line passes through (3,10) and is parallel to y=-9, so, we have something like this:
So, we need to find the yellow line equation.
Standard form:
A straight line equation in standard form is something like this equation:
[tex]Ax+By=C[/tex]To do this, we can start for here:
[tex]\frac{(y-y_1)}{(x-x_1)_{}}=\text{ m}[/tex]Where (x_1, y_1) is a point through which the line passes and m is the slope of the line.
In our case the point is (3,10) and the slope is 0 (since the line is parallel to y=-9):
[tex]\begin{gathered} \frac{(y-10)}{(x-3)_{}}=0 \\ y-10=0 \\ y=10 \end{gathered}[/tex]Slope-intercept form:
This equation is something like this:
[tex]y=mx+b[/tex]Where m is, once again, the slope, and b is the y-intercept (the point where the line cross the y axis).
So, we have:
[tex]\begin{gathered} y=0\cdot x+10 \\ y=10 \end{gathered}[/tex]Answer
[tex]\begin{gathered} \frac{(y-10)}{(x-3)_{}}=\frac{0}{1}\text{ } \\ \\ \text{(y-}10)=0\cdot(x-3) \\ y-10=0\cdot x-0\cdot3 \\ -0x+y=10 \\ 0x+y=10 \\ \\ \text{and} \\ \\ y=0\cdot x+10 \end{gathered}[/tex]
