Q. What is the slope of the function \(y = -2x – 3\)?

Solution — step-by-step

1. Identify the slope-intercept form of a line. In slope-intercept form, a linear function is written as
   $y = m x + b$
   where $m$ is the slope and $b$ is the y-intercept.
2. Write the given function and compare it to the slope-intercept form:
   $y = -2x - 3$
   Compare this with $y = m x + b$. The coefficient of $x$ is the slope.
3. Read off the slope from the coefficient of $x$:
   $m = -2$.
4. (Alternative verification using two points) Find two points on the line, for example:
   • When $x=0$, $y=-3$, so one point is $(0,-3)$.
   • When $x=1$, $y=-5$, so another point is $(1,-5)$.

   Compute the slope between these two points using the rise over run formula:
   $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - (-3)}{1 - 0} = \frac{-2}{1} = -2$,
   which confirms the slope found above.

5. Final answer: the slope of the function $y = -2x - 3$ is
   $-2$.