Question

Which equation represents the line shown in the graph below?

A. y = -5/4 x

B. y = 4/5x

C. y= 5/4x

D. y = -4/5x

Answer 1

Which answers cannot be.
It has a minus slope.
That let's out B and C. They are both wrong. Minus slopes go from lower right to upper left.

How to find out which it is 
Notice that x = 5 and y = -4 is on the given line
So you have two points (0,0) and (5,-4)

slope = (y2 - y1) / (x2 - y1)
slope = (-4 - 0)/ (5 - 0 )
slope = - 4/5

Line
y = - 4/5 x <<<< answer

Answer 2

The equation that represents the line shown in the graph is

D. y = -(4/5)x

Further explanation

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 :

m → gradient of the line

( 0 , c ) → y - intercept

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

$\large {\boxed {m = \frac{y_2 - y_1}{x_2 - x_1}}}$

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

$\large {\boxed {y - y_1 = m ( x - x_1 )} }$

Let us tackle the problem!

From the graph , the line goes through the point ( -5 , 4 ) and ( 0 , 0 ).

Let:

( x₁ , y₁ ) = ( 0 , 0 )

( x₂ . y₂ ) = ( -5 , 4 )

$\texttt{ }$

We can calculate the gradient of the graph by using this following formula:

$m = ( y_2 - y_1 ) \div ( x_2 - x_1 )$

$m = ( 4 - 0 ) \div ( -5 - 0 )$

$m = 4 \div (-5)$

$m = -\frac{4}{5}$

$\texttt{ }$

Next , we can find the equation of the graph by using this following formula:

$y - y_1 = m ( x - x_1 )$

$y - 0 = -\frac{4}{5} ( x - 0 )$

$y = -\frac{4}{5}x$

$\texttt{ }$

Learn more

• Infinite Number of Solutions : https://brainly.com/question/5450548
• System of Equations : https://brainly.com/question/1995493
• System of Linear equations : https://brainly.com/question/3291576

Answer details

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point