The answer that best describes them is:
The slope of f(x) is less than the slope of g(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 :
[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.
This probem is about Slope of Linear Equation.
Let:
f(x) passes following coordinates:
( 0 , -1 ) → ( x₁ , y₁ )
( 3 , 1 ) → ( x₂ , y₂ )
We will use the formula as follows:
[tex]\large {\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}}[/tex]
[tex]m_{f(x)} = \frac{1 - (-1)}{3 - 0}[/tex]
[tex]m_{f(x)} = \frac{2}{3}[/tex]
[tex]\texttt{ }[/tex]
g(x) passes following coordinates:
( 0 , 3 ) → ( x₁ , y₁ )
( 2 , 6 ) → ( x₂ , y₂ )
We will use the formula as follows:
[tex]\large {\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}}[/tex]
[tex]m_{g(x)} = \frac{6 - 3}{2 - 0}[/tex]
[tex]m_{g(x)} = \frac{3}{2}[/tex]
[tex]\texttt{ }[/tex]
[tex]\frac{2}{3} < \frac{3}{2}[/tex]
[tex] m_{f(x)} < m_{g(x)}[/tex]
∴ The slope of f(x) is less than the slope of g(x)
[tex]\texttt{ }[/tex]
Learn more
- Infinite Number of Solutions : https://brainly.com/question/5450548
- System of Equations : https://brainly.com/question/1995493
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Answer details
Grade: High School
Subject: Mathematics
Chapter: Linear Equations
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point
