Answer:
The equation of the line through the points (-5, 2) and (-2, 6) is [tex]y = \frac{4}{3}\cdot x +\frac{26}{3}[/tex].
Step-by-step explanation:
The point-slope form of the equation of the line is defined by this formula:
[tex]y-y_{1} = m\cdot (x-x_{1})[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]m[/tex] - Slope.
[tex]x_{1}[/tex], [tex]y_{1}[/tex] - Coordinates of the first point.
In addition, the slope of the line can be determined in terms of two distinct points:
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] (2)
Where [tex]x_{2}[/tex], [tex]y_{2}[/tex] are the coordinates of the second point.
If we know that [tex]x_{1} = -5[/tex], [tex]y_{1} = 2[/tex], [tex]x_{2} = -2[/tex] and [tex]y_{2} = 6[/tex], then the equation of the line is:
[tex]m = \frac{6-2}{-2-(-5)}[/tex]
[tex]m = \frac{4}{3}[/tex]
[tex]y-2 = \frac{4}{3}\cdot (x+5)[/tex]
[tex]y = \frac{4}{3}\cdot x +\frac{26}{3}[/tex]
The equation of the line through the points (-5, 2) and (-2, 6) is [tex]y = \frac{4}{3}\cdot x +\frac{26}{3}[/tex].
