Given:
Given that the graph of a linear function.
We need to determine the equation of the graph in slope intercept form.
Slope:
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,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the coordinates in the above formula, we get;
[tex]m=\frac{-1-3}{4+4}[/tex]
[tex]m=\frac{-4}{8}[/tex]
[tex]m=-\frac{1}{2}[/tex]
Thus, the slope of the equation is [tex]m=-\frac{1}{2}[/tex]
Value of y - intercept:
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 [tex]b=1[/tex]
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y=mx+b[/tex]
Substituting the slope [tex]m=-\frac{1}{2}[/tex] and the y - intercept [tex]b=1[/tex]
Thus, we get;
[tex]y=-\frac{1}{2}x+1[/tex]
Thus, the equation of the line is [tex]y=-\frac{1}{2}x+1[/tex]
