Question

Which linear equation below represents the line that goes through the point (3.4) and has a slope of 2?

Answer 1

Answer:

Linear equation with a slope of 2 that goes through the point (3, 4) is $y = 2\cdot x -2$.

Step-by-step explanation:

From statement we know the slope of the line and a point contained in it. Using the slope-point equation of the line is the quickest approach to determine the appropriate equation, whose expression is:

$y-y_{o} = m \cdot (x-x_{o})$

Where:

$m$ - Slope, dimensionless.

$x_{o}$, $y_{o}$ - Components of given point, dimensionless.

$x$, $y$ - Independent and dependent variable, dimensionless.

If we know that $m = 2$, $x_{o} = 3$ and $y_{o} = 4$, the linear equation is found after algebraic handling:

1) $y-4 = 2\cdot (x-3)$ Given

2) $y = 2\cdot (x-3) +4$ Compatibility with Addition/Existence of Additive Inverse/Modulative Property

3) $y = 2\cdot x -2$ Distributive Property/$(-a)\cdot b = -a\cdot b$/Definition of sum/Result

Linear equation with a slope of 2 that goes through the point (3, 4) is $y = 2\cdot x -2$.