Question

How do you find the slope and intercept to graph $y = - 3x - 6$?

Answer 1

To solve the above question we first need to identify the shape of the graph corresponding to the given equation $y = - 3x - 6$. Since this equation is linear with respect to both the variables x and y, so the graph of the given equation will be a straight line. For finding the slope and intercept of the given equation, we need to compare the given equation with the general slope-intercept form of a line. By comparing it, we will get the required values of the slope and the intercept.

Complete step-by-step solution:
The equation to be graphed is given in the question as
$y = - 3x - 6$..............................(1)
As can be seen in the above equation, the powers of both the variables x and y in the equation are equal to one. This means that the given equation is linear with respect to both x and y. Thus, the graph of the given equation will represent a straight line.
To determine the slope and the intercept of the straight line, we have to compare the given equation with the slope-intercept form of a line which is given as
$y = mx + c$.............................(2)
On comparing the equations (1) and (2), we get
$m = - 3$ and $c = - 6$

Hence, the slope of the given line is equal to $- 3$ and the intercept (the y intercept) is equal to $- 6$.

Note:
The slope of an equation can also be determined by differentiating it with respect to the independent variable. So we could also differentiate the equation $y = - 3x - 6$ with respect to x to get the value of the slope equal to $- 3$.