The equation of the following line is D. y = -6x
Further explanation
Let the linear equation : [tex]y = mx + c[/tex]
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 :
[tex]\large {\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :
[tex]\large {\boxed{y - y_1 = m ( x - x_1 )} }[/tex]
Let us tackle the problem.
From the attached picture, we can see a straight line through two points , (0,0) and (-½ , 3).
Let :
( 0 , 0 ) → ( x₁ , y₁ )
( -½ , 3 ) → ( x₂ , y₂ )
We can find the equation of solid line passing through points (x₁,y₁) and (x₂,y₂) by using this formula :
[tex]\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}[/tex]
[tex]\frac{y - 0}{3 - 0} = \frac{x - 0}{-\frac{1}{2} - 0}[/tex]
[tex]\frac{y}{3} = \frac{x}{-\frac{1}{2}}[/tex]
[tex]\frac{y}{3} = -2x[/tex]
[tex]y = 3 \times (-2x)[/tex]
[tex]\large {\boxed {y = -6x}}[/tex]
Learn more
- Infinite Number of Solutions : https://brainly.com/question/5450548
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Answer details
Grade: High School
Subject: Mathematics
Chapter: Linear Equations
Keywords: Equation , Line , Variable , Line , Gradient , Point
