Question

Use the point-slope form to find the ewuation of the line through the points (-5,2) and (-2,6)

Answer 1

Answer:

The equation of the line through the points (-5, 2) and (-2, 6) is $y = \frac{4}{3}\cdot x +\frac{26}{3}$.

Step-by-step explanation:

The point-slope form of the equation of the line is defined by this formula:

$y-y_{1} = m\cdot (x-x_{1})$ (1)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$m$ - Slope.

$x_{1}$, $y_{1}$ - Coordinates of the first point.

In addition, the slope of the line can be determined in terms of two distinct points:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ (2)

Where $x_{2}$, $y_{2}$ are the coordinates of the second point.

If we know that $x_{1} = -5$, $y_{1} = 2$, $x_{2} = -2$ and $y_{2} = 6$, then the equation of the line is:

$m = \frac{6-2}{-2-(-5)}$

$m = \frac{4}{3}$

$y-2 = \frac{4}{3}\cdot (x+5)$

$y = \frac{4}{3}\cdot x +\frac{26}{3}$

The equation of the line through the points (-5, 2) and (-2, 6) is $y = \frac{4}{3}\cdot x +\frac{26}{3}$.