Answer:
The equation in slope-intercept form of required line is: [tex]\mathbf{y=-x+2}[/tex]
Step-by-step explanation:
We need to write equation in slope-intercept form to represent the relationship on the graph.
The general equation in slope-intercept form is: [tex]y=mx+b[/tex]
Where m is slope and b is y-intercept
Finding slope using formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\[/tex]
Looking at he graph we have
x_1=0, y_1=2, x_2=1, y_2=1
Putting values in formula and finding slope:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\\\Slope=\frac{1-2}{1-0}\\Slope=\frac{-1}{1}\\Slope=-1[/tex]
So, we get slope m = -1
Using slope m=-1 and point (0,2) we can find y-intercept
[tex]y=mx+b\\2=-1(0)+b\\b=2[/tex]
So, y-intercept b = 2
The equation of line having m=-1 and b=2 will be:
[tex]y=mx+b\\y=-1(x)+2\\y=-x+2[/tex]
The equation in slope-intercept form of required line is: [tex]\mathbf{y=-x+2}[/tex]
