Question

How do you find the slope and intercept of $ - 3x = 6y + 18$?

Answer 1

Hint: Change of form of the given equation will give the slope, y intercept, and x-intercept of the line $ - 3x = 6y + 18$. We change it to the form of y= mx + k to find the slope m and k is the y-intercept of the line y= mx + k as discussed in detail below.

Complete step-by-step solution:
The given equation $ - 3x = 6y + 18$ is of the form ax + by = c. Here a, b, care the constants. We convert the form to y = mx + k. m is the slope of the line.
So, converting the equation we get
$ - 3x = 6y + 18$
$\Rightarrow$$6y = - 3x - 18$
Divide both sides by 6 and we will get-
$\Rightarrow$$y = \left( { - 3x - 18} \right) \times \dfrac{1}{6}$
Take 3 as common from the numerator and further simplify the above equation.
$\Rightarrow$$y = \left( { - x - 6} \right) \times \dfrac{1}{2}$
Expanding the right-hand side of the above equation as given below:
$\Rightarrow$$y = \dfrac{{ - x}}{2} - 3$
When we compare this equation with standard equation of straight-line y=mx+ k, we will get the value of slope $m = \dfrac{{ - 1}}{2}$ and $k = - 3$

Therefore, this gives the slope of line $ - 3x = 6y + 18$ is $\dfrac{{ - 1}}{2}$.
And y-intercept of the line $ - 3x = 6y + 18$ is -3.

Note: In the question we also easily able to draw the graphs of a two variable linear equation where you should express the dependent variable in terms of independent variable and then get two points in the XY plane to draw the graph and also remember that A line parallel the X-axis does not intersect the X-axis at any finite distance and Same goes for lines parallel to the Y-axis.