SAT Question 17d80dc3: Linear Functions answer and explanation with Desmos solution

An equation of a line in the xy-plane can be written in the form $y=mx+b$, where $m$ is the slope of the line and $(0,b)$ is the y-intercept of the line. It’s given that line $k$ has a slope of $5$ and a y-intercept of $(0,-35)$. Therefore, $m=5$ and $b=-35$. Substituting $5$ for $m$ and $-35$ for $b$ in the equation $y=mx+b$ yields $y=5x-35$. The x-intercept of a line in the xy-plane is the point where the line intersects the x-axis, which is a point with a y-coordinate of $0$. Substituting $0$ for $y$ in the equation $y=5x-35$ yields $0=5x-35$. Adding $35$ to both sides of this equation yields $35=5x$. Dividing both sides of this equation by $5$ yields $7=x$. Therefore, the x-coordinate of the x-intercept of line $k$ is $7$.