The equation that represents the line shown in the graph is
D. y = -(4/5)x
<h3>Further explanation</h3>
Solving linear equation mean calculating the unknown variable from the equation.
Let the linear equation : y = mx + c
If we draw the above equation on Cartesian Coordinates , it will be a straight line with :
<em>m → gradient of the line</em>
<em>( 0 , c ) → y - intercept</em>
<em>Gradient of the line could also be calculated from two arbitrary points on line</em><em> ( x₁ , y₁ )</em><em> and </em><em>( x₂ , y₂ ) </em><em>with the formula :</em>
![\large {\boxed {m = \frac{y_2 - y_1}{x_2 - x_1}}}](https://tex.z-dn.net/?f=%5Clarge%20%7B%5Cboxed%20%7Bm%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%7D%7D)
<em>If point </em><em>( x₁ , y₁ )</em><em> is on the line with gradient </em><em>m</em><em> , the equation of the line will be :</em>
![\large {\boxed {y - y_1 = m ( x - x_1 )} }](https://tex.z-dn.net/?f=%5Clarge%20%7B%5Cboxed%20%7By%20-%20y_1%20%3D%20m%20%28%20x%20-%20x_1%20%29%7D%20%7D)
Let us tackle the problem!
From the graph , the line goes through the point ( -5 , 4 ) and ( 0 , 0 ).
Let:
<em>( x₁ , y₁ ) = ( 0 , 0 )</em>
<em>( x₂ . y₂ ) = ( -5 , 4 )</em>
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
We can calculate the gradient of the graph by using this following formula:
![m = ( y_2 - y_1 ) \div ( x_2 - x_1 )](https://tex.z-dn.net/?f=m%20%3D%20%28%20y_2%20-%20y_1%20%29%20%5Cdiv%20%28%20x_2%20-%20x_1%20%29)
![m = ( 4 - 0 ) \div ( -5 - 0 )](https://tex.z-dn.net/?f=m%20%3D%20%28%204%20-%200%20%29%20%5Cdiv%20%28%20-5%20-%200%20%29)
![m = 4 \div (-5)](https://tex.z-dn.net/?f=m%20%3D%204%20%5Cdiv%20%28-5%29)
![m = -\frac{4}{5}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7B4%7D%7B5%7D)
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
Next , we can find the equation of the graph by using this following formula:
![y - y_1 = m ( x - x_1 )](https://tex.z-dn.net/?f=y%20-%20y_1%20%3D%20m%20%28%20x%20-%20x_1%20%29)
![y - 0 = -\frac{4}{5} ( x - 0 )](https://tex.z-dn.net/?f=y%20-%200%20%3D%20-%5Cfrac%7B4%7D%7B5%7D%20%28%20x%20-%200%20%29)
![y = -\frac{4}{5}x](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B4%7D%7B5%7Dx)
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<h3>Learn more</h3>
<h3>Answer details</h3>
Grade: High School
Subject: Mathematics
Chapter: Linear Equations
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point