Question

write an equation of the line through (9, -13) having slope 0. give the answer in standard form. the equation is \boxed{}

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that the slope $m = 0$. So the equation of the line becomes $y=0\times x + b$, which simplifies to $y = b$.

Step2: Find the value of $b$

The line passes through the point $(9,-13)$. Since the equation of the line is $y = b$ (because the slope is 0, it's a horizontal line), and for a horizontal line, all the points on the line have the same $y$ - coordinate. So when $x = 9$, $y=-13$. This means that $b=-13$. So the equation of the line in slope - intercept form is $y=-13$.

Step3: Convert to standard form

The standard form of a line is $Ax+By = C$, where $A$, $B$, and $C$ are integers, and $A\geq0$. Starting from $y=-13$, we can rewrite it as $0x + 1y=-13$.

Answer:

$0x + y=-13$ (or simply $y=-13$ can also be considered in standard form as $0x + 1y=-13$, and since the coefficient of $x$ is 0, we can also write it as $y+ 13=0$ or $0x + y=-13$. The most appropriate standard form here is $0x + y=-13$ or $y=-13$ (usually, we can write it as $y+13 = 0$ or $0x + y=-13$. But the standard form $Ax + By=C$ with $A = 0$, $B = 1$, $C=-13$ is $0x + y=-13$ which can be simplified to $y=-13$)