SAT Question fdee0fbf: Linear Equations In Two Variables answer and explanation with Desmos solution

The $y$-intercept of a line in the $xy$-plane is the ordered pair $(x,y)$ of the point of intersection of the line with the $y$-axis. Since line $k$ intersects the $y$-axis at the point $(0,-6)$, it follows that $(0,-6)$ is the $y$-intercept of this line. An equation of any line in the $xy$-plane can be written in the form $y=mx+b$, where $m$ is the slope of the line and $b$ is the $y$-coordinate of the $y$-intercept. Therefore, the equation of line $k$ can be written as $y=mx-6$. The value of $m$ can be found by substituting the $x$- and $y$-coordinates from a point on the line, such as $(2,2)$, for $x$ and $y$, respectively. This results in $2=2m-6$. Solving this equation for $m$ gives $m=4$. Therefore, an equation of line $k$ is $y=4x-6$. The value of $w$ can be found by substituting the $x$-coordinate, $20$, for $x$ in the equation of line $k$ and solving this equation for $y$. This gives $y=4\times 20-6$, or $y=74$. Since $w$ is the $y$-coordinate of this point, $w=74$.