Question

Write an equation of the line with the given conditions.

$\left(2,5\right)$; slope 3.

Short answer

The equation of the straight line for the given condition is $\mathit{y}\mathbf{=}\mathbf{3}\mathit{x}\mathbf{-}\mathbf{1}$.

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.

$\begin{array}{l}\left(x_1,y_1\right)=\left(2,5\right)\\ m=3\end{array}$

Step 3. Substitute the values to get the required equation.

Substitute the above values in the equation$y-y_1=m\left(x-x_1\right)$

$$\begin{gathered} y-y_1=m\left(x-x_1\right) \\ y-5=3\left(x-2\right) \\ y-5=3x-6 \\ y-5+5=3x-6+5 \\ y=3x-1 \end{gathered}$$

The equation of the straight line is $y=3x-1$.