Part A: Solving for the slope.
Recall that given two points in the line, the slope of a linear function is given by the equation
[tex]\begin{gathered} m = \dfrac{y_2 - y_1}{x_2 - x_1} \\ \text{where} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the two points.} \end{gathered}[/tex]
In this instance we will be using points (0,-4) and (1,-5).
Substitute these two points and we get
[tex]\begin{gathered} (x_1,y_1)=(0,-4) \\ (x_2,y_2)=(1,-5) \\ \\ m = \dfrac{y_2 - y_1}{x_2 - x_1} \\ m=\dfrac{-5-(-4)}{1-0} \\ m=\dfrac{-5+4}{1} \\ m=\frac{-1}{1} \\ m=-1 \end{gathered}[/tex]
Therefore, the slope of the linear function is -1.
Part B: Solving for y-intercept
The y-intercept is the value of y, when x = 0.
In the given table, when x = 0, y = -4. Therefore, the y-intercept of the linear function is -4.
Part C: Equation of the line
The slope-intercept form of a line equation is in the form
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]
As solved earlier, the slope is -1, and the y-intercept is -4.
Substitute m = -1, and b = -4, to the slope-intercept form. The equation of the line therefore is
[tex]\begin{gathered} y=mx+b \\ y=(-1)x+(-4) \\ \\ \text{Simplify and we get} \\ y=-x-4\text{ \lparen final answer\rparen} \end{gathered}[/tex]
