Question

I need help with the problem .1. Find the Y-intercept of the following graph:2. What is the slope of the line?3. What is the Equation the line?

Answer 1

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:

`m=(y_2-y_1)/(x_2-x_1)`

We can pick two points on the graph as shown below:

The coordinates of these points 1 and 2 are:

`\begin{gathered} (x_1,y_1)=(-4,0) \\ (x_2,y_2)=(0,-2) \end{gathered}`

Using these coordinates, we can calculate the slope to be:

`\begin{gathered} m=(-2-0)/(0-\lbrack-4\rbrack)=(-2)/(4) \\ m=-(1)/(2) \end{gathered}`

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:

`\begin{gathered} y=mx+b \\ \text{where } \\ x,y=\text{ variables} \\ m=\text{ slope} \\ b=y-\text{intercept} \end{gathered}`

In the previous questions, we have calculated the slope and y-intercept of the line to be:

`\begin{gathered} b=-2 \\ m=-(1)/(2) \end{gathered}`

Therefore, using these parameters, we have the equation of the line to be:

`\begin{gathered} y=-(1)/(2)x+(-2) \\ y=-(1)/(2)x-2 \end{gathered}`

The equation of the line is y = -¹/₂x - 2