Question

Complete the equation describing howx and y are related.0123V-1 3 71115y = 4x + [?]Enter the answer that belongs in [?].Enter

Answer 1

We will investigate how to determine the y-intercept of an equation of a line.

A general equation of a line is given in a slope-intercept form as follows:

`y\text{ = m}\cdot x\text{ + c}`

Where,

`\begin{gathered} m\colon\text{ slope} \\ c\colon\text{ y-intercept} \end{gathered}`

The slope of the line is already determined and expressed as follows:

`y\text{ = 4x + c}`

To determine the y-intercept of an equation of a line we need a coordinate pair. We are given a table of values through which the line passes. We can use any of the coordinate pair. We will pick the first pair:

`(\text{ 0 , -1 )}`

We will plug in the respective coordinate values in the given equation and solve for y-intercept ( c ) as follows:

`\begin{gathered} -1\text{ = 4}\cdot(0)\text{ + c} \\ c\text{ = -1} \end{gathered}`

Therefore, the value of the y-intercept when plugged in the general equation we have:

`y\text{ = 4x - 1}`