Q4. - Algebra 1

Question

Write an equation in point slope-intercept form that passes through the given point and has the given slope.  

 

$\left(3,-5\right)$, slope $\frac{2}{3}$

Step-by-Step Solution

Answer

The required equation is represented by $y=\frac{2}{3}x-7$.

Step 1. Determine the formula that can be used.

The standard form associated with forms which are slope and point related to the line that is straight is $y-y_1=m\left(x-x_1\right)$ in which the representation of the slope is m and the representation of the point which represents the travelling of the line is $\left(x_1,y_1\right)$ can be used to calculate the required equation.

Step 2. Take the help of the obtained method.

Take the help of obtained standard form represented by $y-y_1=m\left(x-x_1\right)$ in which the required values can be filled by using the provided point as it is in the form of $\left(x_1,y_1\right)$ and the slope.

$$\begin{gathered} y-\left(-5\right)=\frac{2}{3}\left(x-3\right) \\ y=\frac{2}{3}x-2-5 \\ y=\frac{2}{3}x-7 \end{gathered}$$

Step 3. Write the conclusion.

The obtained equation is $y=\frac{2}{3}x-7$ so it is the required equation.