Question

Write the equation in Slope-intercept form with a slope of$\mathbf{-}\frac{\mathbf{2}}{\mathbf{3}}$ and a $\mathit{y}\mathbf{-}$intercept 6.

Short answer

The equation of the line in Slope-intercept is:$\mathit{y}\mathbf{=}\mathbf{-}\frac{\mathbf{2}}{\mathbf{3}}\mathit{x}\mathbf{+}\mathbf{6}$

Step-by-step solution

Step 1. State the concept of ‘Slope-intercept form’.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the $y$-intercept (the $y$-coordinate of the point where the line intersects the$y$-axis).

Step 2. Write the general algebraic expression of slope-intercept form.

The slope-intercept form of a straight line is used to find the equation of a line. For the slope-intercept formula, we have to know the slope of the line and the intercept cut by the line with the $y$-axis.

Consider a straight line of slope $\text{'}m\text{'}$and $y$-intercept $\text{'}b\text{'}$. The slope intercept form equation for a straight line with a slope, $\text{'}m\text{'}$and $\text{'}b\text{'}$as the $y$-intercept can be given as:

$y=mx+b$

Step 3. Find the equation.

Substitute$m=-\frac{2}{3}$ and$b=6$ in $y=mx+b$to get the required equation.

$\begin{array}{c}y=mx+b\\ y=-\frac{2}{3}x+6\end{array}$

Hence, the required equation.