*Correction: The points given on the graph are (-2, -6) and (2, -3)
Answer:
The slope of the line is [tex]m = \frac{3}{4} = 0.75[/tex]
The y-intercept is [tex]\left(0, - \frac{9}{2}\right) = \left(0, -4.5\right)[/tex]
The equation of the line in the slope-intercept form is [tex]y = \frac{3 x}{4} - \frac{9}{2}[/tex] 0.75x−4.5
Step-by-step explanation:
Your input:
Find the equation of a line given two points P=(−2,−6) and [tex]Q = \left(2, -3\right)Q=(2,-3).[/tex]
SOLUTION
The slope of a line passing through two points [tex]P = \left(x_{1}, y_{1}\right)[/tex] and [tex]Q = \left(x_{2}, y_{2}\right)[/tex]
is given by m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].
We have that , [tex]x_{1} = -2[/tex], [tex]y_{1} = -6y[/tex], [tex]x_{2} = 2x[/tex], and [tex]y_{2} = -3y[/tex].
Plug the given values into the formula for a slope:[tex]m = \frac{-3 - \left(-6\right)}{2 - \left(-2\right)} = \frac{3}{4}[/tex]
Now, the y-intercept is [tex]b = y_{1} - m x_{1}[/tex] (or [tex]b = y_{2} - m x_{2}[/tex] , the result is the same).
[tex]b=-6-(\frac{3}{4})*(-2)=-\frac{9}{2}[/tex]
Finally, the equation of the line can be written in the form y = b + m x:
[tex]y = \frac{3 x}{4} - \frac{9}{2}[/tex]
