Answer:
The equation in the slope-intercept form will be:
- [tex]\:y=-\frac{x}{2}-1[/tex]
Step-by-step explanation:
Given
Important Tip:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
- [tex]m[/tex] represents the slope
- [tex]b[/tex] is the y-intercept
In our case,
Step 1 of 2
Determine the y-intercept b
substitute m = -1/2 and (x, y) = (6, -4) in the slope-intercept form of the line equation
[tex]y = mx+b[/tex]
[tex]-4\:=-\:\frac{1}{2}\left(6\right)+b[/tex]
switch sides
[tex]-\frac{1}{2}\left(6\right)+b=-4[/tex]
[tex]-3+b=-4[/tex]
Add 3 to both sides
[tex]-3+b+3=-4+3[/tex]
simplify
[tex]b=-1[/tex]
Thus, the y-intercept b = -1
Step 2 of 2
substitute the values
substitute b = -1 and m = 1/2 in the slope-intercept form of the line equation
[tex]y = mx+b[/tex]
[tex]y=-\frac{1}{2}x+\left(-1\right)[/tex]
[tex]\:y=-\frac{x}{2}-1[/tex]
Conclusion:
Therefore, the equation in the slope-intercept form will be:
[tex]\:y=-\frac{x}{2}-1[/tex]
The graph of the line equation is also attached.
