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:

$m=\frac{y_2-y_1}{x_2-x_1}$

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:

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{5-3}{4-0} \\ \\ m=\frac{2}{4} \\ \\ m=\frac{1}{2} \end{gathered}$

So the equation of line become,

$\begin{gathered} y=mx+b \\ \\ y=\frac{1}{2}x+b \end{gathered}$

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

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

Y-intercept is:

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

Final equation of line is:

$\begin{gathered} y=mx+b \\ \\ y=\frac{1}{2}x+3 \end{gathered}$