Answer:
[tex]y=-x+3[/tex]
Step-by-step explanation:
Let's start by defining what slope-intercept form is. Slope-intercept form is:
y=mx+b
Where...
"y" = y-coordinate of any point on the line
"m" = slope of the line
"x" = x-coordinate of any point on the line
"b" = y-intercept (where the line intercepts the y-axis)
Let's start by finding the y-intercept. As stated above, the y-intercept is where the line intercepts the y-axis. Looking at the graph, we can tell that in this case, it is (0, 3).
Note that the y-intercept (b) is represented by ONLY the y-value, which in this case is 3.
Now, let's find the slope. Start by taking ANY two points on the line. Let's use (0, 3) and (1, 2).
The formula for slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]y_1, y_2:$ Values for the two y-coordinates\\x_1, x_2:$ Values for the two x-coordinates[/tex]
Substitute the given points into the equation:
[tex]m=\frac{2-3}{1-0}=\frac{-1}{1}=-1[/tex]
The slope is -1.
Finally, we substitute our slope and y-intercept back into the equation and get:
[tex]y=-x+3[/tex]
