Sketching linear graphs My question for today is how should I work out this question:

Sketch the following linear graphs.
  $$5x + 2y - 10 = 0, \ \ \ x\in[-4,\infty)$$

I have no idea how to start this question. I am studying for a math methods sac after the holidays and this is the last question that I'm stuck on. Feel free to use other examples if you have any. Thanks
 A: Plotting graphs is fundamental to mathematics, and is key to understanding the behaviour of polynomial, trigonometric, rational and exponential functions. This is the fundamental intuition behind calculus, via the differentiation of a given function in order to determine it's relative rate at some input; we call this it's slope. 
Furthermore, in regards to your question, it models a linear polynomial function of degree 1. 
So algebraically, we have: $5x+2y-10=0$
A function is defined as a mathematical relation, which maps some input, in this case $x$, to a corresponding output. In the above example, $x$ can vary as any real number, and thus we say $x\in R$ ("x is an element of the reals"). So we can simply solve for the corresponding output "$y$", and see how it varies with respect to its argument $x$.
Solving for y, we have:
$5x+2y-10=0 \Rightarrow 2y=10-5x \Rightarrow y=5-\frac {5x}2$
Now that we have the polynomial function in terms of its mapping y/f(x), and noting the function has a constant rate of change (slope) for all $x$ of its domain, all we must find is the functions y-intercept, x-intercept, and slope.
Solving for the x-intercept:
The x-intercept is where the function y, intersects the x-axis. Commonly called the root or zero of the function, this mathematically means at some value of $x$, $y$ must equal $0$. So simply set $y=0$ and solve for $x$.
$y=5-\frac {5x}2 \Rightarrow0=5-\frac {5x}2 \Rightarrow-5=-\frac{5x}2\Rightarrow5=\frac{5x}2\Rightarrow x=2$
Therefore, the x-intercept or single root of the function is at the point (2,0)
Likewise, the y-intercept is the direct opposite of the x-intercept, such that the function intersects the y-axis at $x=0$. So simply set $x=0$ and solve for $y$.
$y=5-\frac {5x}2 \Rightarrow y=5-\frac {5(0)}2 \Rightarrow y=5$
Therefore, the y-intercept of the function is at the point (0,5).
To find the slope (rate of change of the function), we simply take the change in its $y$ position over the change in its $x$ position. This is done by taking the difference of any two of its y outputs, divided by their respective x inputs.
Another realization, because this function is linear, is that the slope always equals the coefficient of the variable x. Because $y=5-\frac {5x}2$, that implies the function has a negative slope, mathematically equivalent to $\frac {-5}2$. 
Finally, create a 2-dimensional Cartesian plane (graph), plotting your x and y intercepts, and connect them with a straight line, extending the left side of the line up to the point x=-4, and the right side of the line to infinity. (To show infinity, just use an arrow at the end of your plotted line in the direction it's travelling).
I recommend using the software https://www.desmos.com/calculator, and typing in your original question. This should give you an intuitive sense as to what I just explained.
Hope this helps! 
