Question

What is the equation for this line in the format Y =MX + B? Please see attached photo

Answer 1

Given:

Find-:

Equation of line

Explanation-:

The general equation of a line is:

`y=mx+b`

Where,

`\begin{gathered} m=\text{ Slope} \\ \\ b=\text{ Y-intercept} \end{gathered}`

The slope of line is:

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

Where,

`\begin{gathered} (x_1,y_1)=\text{ First point} \\ \\ (x_2,y_2)=\text{ Second point} \end{gathered}`

So, slope of line is:

`\begin{gathered} (x_1,y_1)=(0,3) \\ \\ (x_2,y_2)=(4,5) \end{gathered}`

Slope is:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \\ m=(5-3)/(4-0) \\ \\ m=(2)/(4) \\ \\ m=(1)/(2) \end{gathered}`

So the equation of line become,

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

If the line pass (0,3) than it satisfied the equation of line so,

`(x,y)=(0,3)`

Y-intercept is:

`\begin{gathered} y=mx+b \\ \\ y=(1)/(2)x+b \\ \\ 3=(1)/(2)(0)+b \\ \\ b=3 \end{gathered}`

Final equation of line is:

`\begin{gathered} y=mx+b \\ \\ y=(1)/(2)x+3 \end{gathered}`