QUESTION 1
The y-intercept of a graph refers to the y-coordinate or value when the graph intersects the y-axis. This is the y-value at x = 0.
The graph in the problem has the y-coordinate as shown in the image below:
That point has a y-value of -2 by counting the boxes.
Therefore, the y-intercept is -2.
QUESTION 2
The slope of a line refers to the rate of change of the values in the y-axis to that in the x-axis. This can be written out mathematically as a formula to be:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We can pick two points on the graph as shown below:
The coordinates of these points 1 and 2 are:
[tex]\begin{gathered} (x_1,y_1)=(-4,0) \\ (x_2,y_2)=(0,-2) \end{gathered}[/tex]
Using these coordinates, we can calculate the slope to be:
[tex]\begin{gathered} m=\frac{-2-0}{0-\lbrack-4\rbrack}=\frac{-2}{4} \\ m=-\frac{1}{2} \end{gathered}[/tex]
The slope of the line is -¹/₂.
QUESTION 3
The equation of a straight line in the slope-intercept form is written out in the form:
[tex]\begin{gathered} y=mx+b \\ \text{where } \\ x,y=\text{ variables} \\ m=\text{ slope} \\ b=y-\text{intercept} \end{gathered}[/tex]
In the previous questions, we have calculated the slope and y-intercept of the line to be:
[tex]\begin{gathered} b=-2 \\ m=-\frac{1}{2} \end{gathered}[/tex]
Therefore, using these parameters, we have the equation of the line to be:
[tex]\begin{gathered} y=-\frac{1}{2}x+(-2) \\ y=-\frac{1}{2}x-2 \end{gathered}[/tex]
The equation of the line is y = -¹/₂x - 2
