i need help on these problems, they dont make sence to me, and i have to get this finished pretty fast, can anyone help me please? appreciate it much
1. y=x/3
2. y=-3x-2
1. y=x/3
2. y=-3x-2
Two linear equations (i.e., their graphs are straight lines).
y = mx + b is the most common form you will see.
m is the slope or "rise over run".
b is the y-intercept or where the graph crosses the y-axis when x = 0.
[1] m = 1/3, b = 0
[2] m = -3, b = -2
The slope can be determined by use two points (x1, y1), (x2, y2):
(y2 - y1) / (x2 - x1)
Want more?
Think of the Pythaorean Theorem: c^2 = a^2 + b^2 where (c) is the length of a hypotenuse (the longest side) of a right triangle, and (a) and (b) are the lengths of the other two sides.
Form this information you can also derive the distance formula (point-to-point on a graph), the midpoint formula, and the slope of a line.
It is a good mnemonic device.
The slope is also the "tangent" to the angle opposite the right angle if you use the two points as two ends of the diagonal of a right triangle, and then draw the rest of a right triangle using that diagonal.
That may sound complicated, but a picture would make it very clear. By the time I downloaded a picture, you may have already drawn a right triangle for yourself.
One of these days this information about a right triangle will ease your understanding when you get into differential calculus.
For #1, to find the x intercept, set y=0:
$\displaystyle 0=\frac{1}{3}x \implies \color{red}\boxed{x=0}$
to find the y intercept, set x=0:
$\displaystyle y=\frac{1}{3}(0) \implies \color{red}\boxed{y=0}$
Thus, the coordinates of the x intercept and y intercept are the same : $\displaystyle \color{red}\boxed{(0,0)}$.
The graph below verifies our answer:
For #2, to find the x intercept, set y=0:
$\displaystyle 0=-3x-2 \implies \color{red}\boxed{x=-\frac{2}{3}}$
to find the y intercept, set x=0:
$\displaystyle y=-3(0)-2 \implies \color{red}\boxed{y=-2}$.
Thus, the x intercept is $\displaystyle \color{red}\boxed{\left(-\frac{2}{3},0\right)}$ and the y intercept is $\displaystyle \color{red}\boxed{(0,-2)}$
The graph below verifies our answer.