Question

1Choose the equation that matches the table below.X-101331521Ny-5-27O y = -7x+5O y = 5xOy=3x-2Oy=x-2

Answer 1

Given:

The coordinates are:

Find-:

The equation of a line

Explanation-:

The general equation is:

`y=mx+c`

Where,

`\begin{gathered} m=\text{ Slope} \\ \\ (x,y)=\text{ Coordintes of line} \\ \\ c=\text{ y-intercept} \end{gathered}`

The formula of the slope is:

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

Choose any two points from the chart is:

`\begin{gathered} (x_1,y_1)=(-1,-5) \\ \\ (x_2,y_2)=(0,-2) \end{gathered}`

Then the slope is:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \\ m=(-2-(-5))/(0-(-1)) \\ \\ m=(-2+5)/(0+1) \\ \\ m=(3)/(1) \\ \\ m=3 \end{gathered}`

If the slope of the line is 3, then the equation becomes:

`\begin{gathered} y=mx+c \\ \\ y=3x+c \end{gathered}`

The value of "c" is:

Choose any one point.

`(x,y)=(0,-2)`

The value of "c" is:

`\begin{gathered} y=3x+c \\ \\ (x,y)=(0,-2) \\ \\ -2=3(0)+c \\ \\ -2=0+c \\ \\ c=-2 \end{gathered}`

The equation of line is:

`\begin{gathered} y=mx+c \\ \\ y=3x+(-2) \\ \\ y=3x-2 \end{gathered}`

The equation of line is y = 3x-2