Question

the graph for one equation in a system of equations is shown below.
enter a second equation for the system so that the system has infinitely many solutions.

Explanation:

Step1: Find slope of given line

The line passes through $(0,5)$ and $(6,0)$. Slope $m=\frac{0-5}{6-0}=-\frac{5}{6}$

Step2: Write line's slope-intercept form

Using $y=mx+b$, $b=5$, so $y=-\frac{5}{6}x+5$

Step3: Scale to get equivalent equation

Multiply all terms by 6: $6y=-5x+30$, rearrange to $5x+6y=30$
(Any non-zero scalar multiple works, e.g., multiply by 2: $10x+12y=60$)

Answer:

$\boldsymbol{5x+6y=30}$ (or any non-zero multiple of this equation, e.g., $10x+12y=60$)