We have a line defined by two points, P(-4,9) and Q(12,1).
Knowing two points of the line, we can calculate the slope with the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
In this case, the slope will be:
[tex]\begin{gathered} m=\frac{y_Q-y_P}{x_Q-x_P} \\ m=\frac{1-9}{12-(-4)}=\frac{-8}{12+4}=-\frac{8}{16}=-\frac{1}{2} \end{gathered}[/tex]
With the slope and one point we can express the equation in slope-point form:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-y_Q=m(x-x_Q) \\ y-1=-\frac{1}{2}(x-12) \\ y=-\frac{1}{2}x+\frac{12\cdot1}{2}+1 \\ y=-\frac{1}{2}x+6+1 \\ y=-\frac{1}{2}x+7 \end{gathered}[/tex]
The x-intercept is the value of x that makes the function f(x) become 0.
In this case, we have to find x so that y = 0.
We can replace y in the equation and calculate x as:
[tex]\begin{gathered} y=0 \\ -\frac{1}{2}x+7=0 \\ -\frac{1}{2}x=-7 \\ x=-7\cdot(-2) \\ x=14 \end{gathered}[/tex]
Then, for the x-intercept is x = 14.
Answer:
a) The equation of the line is y = (-1/2)*x+7
b) The x-intercept is x = 14.
