[tex]y\text{ = }\frac{-3}{2}x\text{ + 6}[/tex]
Explanation:
The y-intercept is the value of y when x = 0
To identify y-intercept on a graph, we will check for the the value of y when the line crosses the y axis
From the graph, the line crosses the y axis at y = 6
Hence, the y-intercept is 6
To get the slope, we will pick any two points on the line.
Using points (0, 6) and (4, 0)
Applying the slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} x_1=0,y_1=6,x_2=4,y_2\text{ = }0 \\ m\text{ = }\frac{0\text{ - 6}}{4\text{ - 0}} \\ m\text{ = }\frac{-6}{4} \\ m\text{ = slope = -3/2} \end{gathered}[/tex]
NOTE: the slope is negative because it is going from up to down (moving downwards)
The equation of slope in intercept form: y = mx + b
m = slope = -3/2
b = y-intercept = 6
The equation in y-intercept becomes:
[tex]y\text{ = }\frac{-3}{2}x\text{ + 6}[/tex]
