Question

find the equation of the line write in slope intercept form and in standard form. 1.m = -5, b = 1
2.(1,-2),(3,3)​

Answer 1

Answer:

the equqtio of any straight line can be writen as y=m×+e

Answer 2

Answer:

Equations of the lines in slope-intercept form and standard form are given below,

1. $y=-5x+1$

   $5x+y=1$

2. $y=5x-7$

   $5x-y=7$  

3. $y=\dfrac{5x}{2}+5$  

    $\dfrac{-5x}{2}+y=5$

4. $y=\dfrac{7x}{2}-7\end{array}$

  $\dfrac{7x}{2}-y=7$

Step-by-step explanation:

The question is to find the equation of the line in slope-intercept form and standard form.

1. m=-5, b=1

2. (1,2) and (3,3)

3. (-2,0) and (0,5)

4. a=2, b=-7

The equation to find the equation of the line is as follows,

        $y-y_{1}=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\left( x-x_{1}\right)$  

Here $m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$ is the slope of the line.

 $y=mx+b$ is the slope-intercept form. And $Ax+By=C$ is the standard form.

The solutions are as follows,

1. m=-5, b=1

    In this case, we can directly apply the values to the equation to get the answer.

        $y=mx+b$

        $y=-5x+1$  → Slope-intercept form

By rearranging the slope-intercept form we will get the standard form.

That is,    

            $5x+y=1$

2. (1,2) and (3,3)

Here $x_1=1,\ y_1=-2,\ x_2=3,\ and\ y_2=3$

by substituting we get as follows,

   $\begin{array}{l}y+2=\dfrac{3+2}{2-1}\left(x-1\right)\\\\y+2=5\left(x-1\right)=5x-5\\\\y=5x-5-2\end{array}$

    $y=5x-7$    → Slope-intercept form

  $-5x+y=-7$

or   $5x-y=7$   → Standard form

3. (-2,0) and (0,5)

  Here $x_1=-2,\ y_1=0,\ x_2=0,\ and\ y_2=5$. Then,

      $\begin{array}{l}y-0=\dfrac{5-0}{0+2}\left(x+2\right)\\\\y=\dfrac{5}{2}\left(x+2\right)\\\end{array}$

     $y=\dfrac{5x}{2}+5$  → Slope-intercept form

   

      $\dfrac{-5x}{2}+y=5$  → Standard form

4. a=2, b=-7

            In this case, a=2 means x₁=2 and y₁=0 , and b=-7 means x₂=0 and y₂=-7.

Therefore,

       $\begin{array}{l}y-0=\dfrac{-7-0}{0-2}\left(x-2\right)\\\\y=\dfrac{-7}{-2}\left(x-2\right)\\\\y=\dfrac{7x}{2}-7\end{array}$→ Slope-intercept form

     $\dfrac{7x}{2}-y=7$   → Standard form

These are the answers to the questions.