Solution:
The provisional equation of the line with slope -4/3 that passes through the point (-4,2) is:
[tex]y\text{ = -}\frac{4}{3}x+b[/tex]to find b, we can replace in the previous equation, the coordinates of any point of the line and solve for b. For example, we can take the point (x,y)=(-4,2) and we obtain the following equation:
[tex]2\text{ = -}\frac{4}{3}(-4)+b[/tex]solving for b, we get:
[tex]b\text{ = -}\frac{10}{3}[/tex]thus, the equation of the line is:
[tex]y\text{ = -}\frac{4}{3}x-\frac{10}{3}[/tex]in function notation, this is equivalent to:
[tex]f(x)\text{ = -}\frac{4}{3}x-\frac{10}{3}[/tex]If we graph this function, we obtain the graph of the line:
and, to obtain three points on the line, we can use the formula of the line like this:
for x = 1, then:
[tex]y=f(1)\text{ = -}\frac{4}{3}-\frac{10}{3}=-\frac{14}{3}[/tex]and we obtain the point :
[tex]C=(x,y)=(1,-\frac{14}{3})[/tex]for x = 2, then:
[tex]y=f(2)\text{ = -}\frac{4}{3}(2)-\frac{10}{3}=-6[/tex]and we obtain the point :
[tex]A=(x,y)=(2,-6)[/tex]for x = 3, then:
[tex]y=f(3)\text{ = -}\frac{4}{3}(3)-\frac{10}{3}=-\frac{22}{3}[/tex]and we obtain the point :
[tex]B=(x,y)=\text{ (3,-}\frac{22}{3}\text{)}[/tex]the plot of these three points on the line is:
