Question

Which equation represents the line shown in the graph below?

Answer 1

The equation that represents the line shown in the graph is:

B. y = -3x + 2

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 ( -1 , 5 ) and ( 0 , 2 ).

Let:

( x₁ , y₁ ) = ( 0 , 2 )

( x₂ . y₂ ) = ( -1 , 5 )

$\texttt{ }$

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

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

$m = ( 5 - 2 ) \div ( -1 - 0 )$

$m = 3 \div (-1)$

$m = -3$

$\texttt{ }$

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

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

$y - 2 = -3 ( x - 0 )$

$y - 2 = -3x$

$y = -3x + 2$

$\texttt{ }$

Learn more

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

Answer details

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

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

Answer 2

The equation used to for slope intercept form is commonly used. 

y = mx + b

Let us find the y-intercept first.

The place where the line crosses the y axis is 2.

y = mx + 2

Now, find the slope.

Find two points on the line, then solve.

$m = \frac{y2 - y1}{x2 - x1}$

Alright, I found two points on the line:-  (-2,8) and (2, -4)

$m= \frac{-4 - 8}{2--2}$

m = -12/4
m = -3

The slope is -3. The y-intercept is 2

Lets put them into the equation

y = -3x + 2

Final answer:  B.    y = -3x + 2