<u>Given:</u>
Given that the graph of a linear function.
We need to determine the equation of the graph in slope intercept form.
<u>Slope</u>:
Consider any two coordinates from the equation of the line to determine the slope.
Let the two coordinates are (-4,3) and (4,-1)
The slope can be determined using the formula,
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Substituting the coordinates in the above formula, we get;
![m=\frac{-1-3}{4+4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-1-3%7D%7B4%2B4%7D)
![m=\frac{-4}{8}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-4%7D%7B8%7D)
![m=-\frac{1}{2}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B1%7D%7B2%7D)
Thus, the slope of the equation is ![m=-\frac{1}{2}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B1%7D%7B2%7D)
<u>Value of y - intercept:</u>
The value of y - intercept is the value of y when x = 0.
Hence, from the graph, it is obvious that the value of y when x = 0 is 1.
Hence, the value of y - intercept is 1.
Thus, y - intercept is ![b=1](https://tex.z-dn.net/?f=b%3D1)
<u>Equation of the line:</u>
The equation of the line can be determined using the formula,
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Substituting the slope
and the y - intercept ![b=1](https://tex.z-dn.net/?f=b%3D1)
Thus, we get;
![y=-\frac{1}{2}x+1](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B2%7Dx%2B1)
Thus, the equation of the line is ![y=-\frac{1}{2}x+1](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B2%7Dx%2B1)