Respuesta :
The points are A (-8.75;9), B(9,-5.833) and the slope for both equations are [tex]-\frac{2}{3}[/tex]
Step-by-step explanation:
Step 1; The given equation is y = [tex]-\frac{2x}{3}[/tex] + [tex]\frac{1}{6}[/tex]. Assume the unknown x coordinate is x and the unknown y coordinate is y so the points become A(x;6), B(9;y). For point A we calculate the value of x and in point B we calculate the value of y. So by substituting the first point A(x;6) in the equation, we get
y = [tex]-\frac{2x}{3}[/tex] + [tex]\frac{1}{6}[/tex], 6 = [tex]-\frac{2x}{3}[/tex] + [tex]\frac{1}{6}[/tex],6 - [tex]\frac{1}{6}[/tex] = [tex]-\frac{2x}{3}[/tex] , [tex]-\frac{3}{2}[/tex](6 - [tex]\frac{1}{6}[/tex]) = x, x = -8.75
By substituting the second point B(9;y) in the equation we get
y = [tex]-\frac{2x}{3}[/tex] + [tex]\frac{1}{6}[/tex], y = [tex]-\frac{18}{3}[/tex]+ [tex]\frac{1}{6}[/tex] = -6 + [tex]\frac{1}{6}[/tex] = -5.8333.
So the points are A (-8.75;9), B(9,-5.833).
Step 2; Slope is given by the expression m in the equation y = mx + b.
In this equation y = [tex]-\frac{2x}{3}[/tex] + [tex]\frac{1}{6}[/tex], m = [tex]-\frac{2}{3}[/tex] and b = [tex]\frac{1}{6}[/tex]. So the slope, m = [tex]-\frac{2}{3}[/tex].
