Question

Write$y+3=\frac{1}{2}\left(x-5\right)$in standard form.

Short answer

The equation of the straight line for the given condition is $\mathit{y}\mathbf{-}\left(-3\right)\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left(x-5\right)$.

Step-by-step solution

Step 1. State the concept of a straight line.

The standard form of slope and intercept form of the straight line is $y=mx+c$.

Here, $m$is the slope of the straight line and $c$is the $y$-intercept of the equation.

Step 2. State the equation of a line slope-point form.

The standard form of slope and point form of the straight line is$y-y_1=m\left(x-x_1\right)$

Here $m$is the slope of the straight line and is the point from which the straight line passes.

$$\begin{gathered} \left(x_1,y_1\right)=\left(5,-3\right) \\ m=\frac{1}{2} \end{gathered}$$

Step 3. Simplify the equation to get the required equation.

Converting the given equation in the standard form.

$$\begin{gathered} y+3=\frac{1}{2}\left(x-5\right) \\ y-\left(-3\right)=\frac{1}{2}\left(x-5\right) \end{gathered}$$

The equation of the straight line is $y-\left(-3\right)=\frac{1}{2}\left(x-5\right)$.