Question

How do you write $3y + 6x = 3$ into slope-intercept form?

Answer 1

Hint: In this question, we will write the given equation in terms of general slope-intercept form. We know that the equation in the slope-intercept will be in the form like $y = mx + b$ by moving x coordinate to the right side. After that, take common from both sides. Then, cancel out the common factors to get the desired result.

Complete step-by-step solution:
In two-dimensional geometry, the equation of the line in slope-intercept form can be written as,
$y = mx + c$
Where x is the value of x-coordinate, and y is the value of y-coordinate.
Here, m represents the slope of the lines and c represents the y-intercept of the line.
In a line, the slope of the line is the value of the tangent function for the angle which a given line makes with the x-axis in the anticlockwise direction.
And, the y-intercept of a line is the point on the y-axis. The given line intersects the y axis.
Now, the given line in a question is,
$ \Rightarrow 3y + 6x = 3$
Now, subtract $6x$ from both sides,
$ \Rightarrow 3y + 6x - 6x = 3 - 6x$
Simplify the terms,
$ \Rightarrow 3y = - 6x + 3$
Now take 3 common from the right side,
$ \Rightarrow 3y = 3\left( { - 2x + 1} \right)$
Divide both sides by 3,
$ \Rightarrow y = - 2x + 1$

Hence, the equation of the line $3y + 6x = 3$ in slope-intercept form is $y = - 2x + 1$.

Note: In this question, it is important to note here that $y = mx + b$ is the form called the slope-intercept form of the equation of the line. It is the most popular form of the straight line. Many find this useful because of its simplicity. One can easily describe the characteristics of the straight line even without seeing its graph because the slope and y-intercept can easily be defined or read off from this form. The slope m measures how steep the line is with respect to the horizontal. Let us consider two points $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$ found in the line, the slope can be written as, $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$. The y-intercept b is the point where the line crosses the y-axis.