Question

What is an equation of the line that passes through the points (0, 3) and (5,-3)?

Answer 1

Answer:

The equation of the line that passes through the points (0, 3) and (5, -3) is $y = -\frac{6}{5}\cdot x +3$.

Step-by-step explanation:

From Analytical Geometry we must remember that a line can be formed after knowing two distinct points on Cartesian plane. The equation of the line is described below:

$y = m\cdot x + b$ (Eq. 1)

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$m$ - Slope, dimensionless.

$b$ - y-Intercept, dimensionless.

If we know that $(x_{1},y_{1}) = (0,3)$ and $(x_{2},y_{2})=(5,-3)$, the following system of linear equations is constructed:

$b = 3$ (Eq. 2)

$5\cdot m + b = -3$ (Eq. 3)

The solution of the system is: $b = 3$, $m = -\frac{6}{5}$. Hence, we get that equation of the line that passes through the points (0, 3) and (5, -3) is $y = -\frac{6}{5}\cdot x +3$.