Question

a written description of a system of linear equations is given. the first linear equation has a slope of 9 and a y-intercept of -1. the second linear equation has a slope of -9 through the point (-5, -1). write the system of equations. options: 1. $y = 9x + 1$; $y + 1 = -9(x - 5)$ 2. $y = 9x + 1$; $y - 1 = -9(x - 5)$ 3. $y = 9x - 1$ (and the rest of the third option is cut off but likely has the second equation for the system)

Explanation:

Step1: Find the first equation

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given that the first line has a slope $m = 9$ and a y - intercept $b=-1$. Substituting these values into the slope - intercept form, we get the first equation: $y=9x - 1$.

Step2: Find the second equation

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line. The second line has a slope $m=-9$ and passes through the point $(-5,-1)$. Here, $x_1=-5$ and $y_1 = - 1$. Substituting these values into the point - slope form:
\[

$$\begin{align*} y-(-1)&=-9(x - (-5))\\ y + 1&=-9(x + 5) \end{align*}$$

\]
(Note: It seems there might be a typo in the original options, but based on the calculation of the first equation, the first equation should be $y = 9x-1$)

Answer:

The first equation of the system is $y = 9x-1$. For the second equation, using the point - slope form with $m=-9$ and the point $(-5,-1)$, we get $y + 1=-9(x + 5)$. If we assume there was a typo in the options and we only consider the first equation part for now, the first equation of the system is $y=9x - 1$.