To be able to determine the equation of the line, we need to have a y-intercept and its slope.
The y-intercept is the value of y when x = 0. In the table that we have, when x = 0, g(x) = 5, hence, our y-intercept is 5.
Next, let's determine the slope. To determine the slope, we need two points and the formula below:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's make use of the points (0, 5) and (5, -10). These will be our (x₁, y₁) and (x₂, y₂). Let's plug these values to the slope formula above.
[tex]\text{slope}=\frac{-10-5}{5-0}=-\frac{15}{5}=-3[/tex]Hence, the slope of the line is -3.
Now that we have slope = -3 and y-intercept = 5, we can now use the slope-intercept equation of the line that is:
[tex]y=mx+b[/tex]where m = slope and b = y-intercept.
[tex]y=-3x+5[/tex]Answer: The equation of the line is g(x) = -3x + 5.
Note that g(x) = y.
