Let the slope of line $s$ be $m_s$. Since line $r$ has slope $-\dfrac12$ and is perpendicular to line $s$, set up an equation using $-\dfrac12 \cdot m_s$ and $-1$.

Once you know the slope of line $s$, remember that a point like $(0,7)$ on the y-axis gives you the y-intercept. How do slope and y-intercept fit into the form $y = mx + b$?

In Desmos, type the equation of line $r$ using point-slope form, for example: y - 2 = -0.5(x - 3). This will draw line $r$ through $(3,2)$ with slope $-\tfrac12$.

On new lines in Desmos, enter each option:

• y = -0.5x + 7
• y = 2x - 7
• y = 2x + 7
• y = -0.5x - 7 This will show all four possible lines along with line $r$.

Look at where each of the four candidate lines crosses the y-axis (where $x=0$). Identify which line(s) pass through the point $(0,7)$ shown on the grid.

Among the line(s) that cross the y-axis at $(0,7)$, compare them with line $r$. In Desmos, note the slopes from the equations you typed: the correct line will have a slope that is the negative reciprocal of $-\tfrac12$, and its graph will form a right angle with line $r$.

Perpendicular lines in the coordinate plane have slopes that are negative reciprocals of each other. That means if line $r$ has slope $m_r$ and line $s$ has slope $m_s$, then

You are told that line $r$ has slope $m_r=-\dfrac12$. Use this to find the slope of line $s$.

Plug $m_r=-\dfrac12$ into the perpendicular-slope relationship:

Solve this equation:

• Multiply both sides by $-2$:

So line $s$ has slope $2$.

A line with slope $m$ and y-intercept $b$ can be written in slope-intercept form as $y = mx + b$.

Line $s$ intersects the y-axis at $(0,7)$, so its y-intercept is $b = 7$. Using the slope $m = 2$ from the previous step, substitute into $y = mx + b$:

Therefore, the equation of line $s$ is $y=2x+7$.