Answer:
An equation in slope-intercept form of the line will be
- [tex]y\:=\frac{1}{2}x-\frac{1}{2}[/tex]
Step-by-step explanation:
The slope-intercept form of the line equation
y = mx+b
where m is the slope and b is the y-intercept
Given the points
Finding the slope between (-1,-1) and (1,0)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-1,\:-1\right),\:\left(x_2,\:y_2\right)=\left(1,\:0\right)[/tex]
[tex]m=\frac{0-\left(-1\right)}{1-\left(-1\right)}[/tex]
[tex]m=\frac{1}{2}[/tex]
substituting m = 1/2 and (-1, -1) in the slope-intercept form of the line equation to determine the y-intercept
[tex]y = mx+b[/tex]
[tex]-1=\frac{1}{2}\left(-1\right)+b[/tex]
[tex]-\frac{1}{2}+b=-1[/tex]
Add 1/2 to both sides
[tex]-\frac{1}{2}+b+\frac{1}{2}=-1+\frac{1}{2}[/tex]
[tex]b=-\frac{1}{2}[/tex]
substituting m = 1/2 and b = -1/2 in the slope-intercept form of the line equation
[tex]y = mx+b[/tex]
[tex]y\:=\frac{1}{2}x+\left(-\frac{1}{2}\right)[/tex]
[tex]y\:=\frac{1}{2}x-\frac{1}{2}[/tex]
Therefore, an equation in slope-intercept form of the line will be
- [tex]y\:=\frac{1}{2}x-\frac{1}{2}[/tex]
