um could anyone plz help me with this queston thats on an exam tommorow....and i need at least a B+....
y= 4√(x+4) -2
y= ⅔x +7
simultaneous equation....i need to sketch a graph, label intercepts and state their value
thx in advance....
have you tried to graph that on a calculator or something.
The second one is a straight line
the intercepts for the second equation is y is 7 and x is 10. I just graphed this into my calculator so it is right and the other equation is crazy I am still trying to work it out.
1) Sketch a graph : just plug in $\displaystyle x = -3, -2, -1, 0, 1, 2, 3$ and get the corresponding $\displaystyle y$ values. Then ... plot. Note that for the second one only two points are required since it is the equation of a line.
2) Label intercepts : that shouldn't be too hard, for the x-intercepts just set $\displaystyle y = 0$ and solve for $\displaystyle x$ in both cases, for the y-intercepts just set $\displaystyle x = 0$ and solve for $\displaystyle y$ in both cases. You therefore get their values which you can then sketch.
As you mentioned "simultaneous equations" I assume you need to solve the system at some point (know where the two curves intersect). You can apply the following method :
Just set $\displaystyle 4 \sqrt{x + 4} - 2 = \frac{2}{3} x + 7$ and solve for $\displaystyle x$ :
$\displaystyle 4 \sqrt{x + 4} - 2 = \frac{2}{3} x + 7$
$\displaystyle 4 \sqrt{x + 4} = \frac{2}{3} x + 9$
$\displaystyle \left ( 4 \sqrt{x + 4} \right ) ^2 = \left ( \frac{2}{3} x + 9 \right ) ^2$
$\displaystyle 16(x + 4) = \left ( \frac{2}{3} x \right )^2 + \frac{36}{3} x + 9^2$
$\displaystyle 16x + 64 = \frac{4}{9} x^2 + 12x + 81$
$\displaystyle 0 = \frac{4}{9} x^2 - 4x + 17$
$\displaystyle 9 \times 0 = 9 \left ( \frac{4}{9} x^2 - 4x + 17 \right )$
$\displaystyle 0 = 4 x^2 - 36x + 153$
$\displaystyle 4 x^2 - 36x + 153 = 0$
Calculate the discriminant :
$\displaystyle \Delta = b^2 - 4ac = (-36)^2 + 4 \times 4 \times 153 = -1152$
It is negative therefore this equation has no real solution for $\displaystyle x$, thus the two curves (the curve and the line) never meet (never intersect).
Does it make sense ?