Question

How do you find the slope and y-intercept of $3y = - 6x + 9$?

Answer 1

The slope of a line in graph is the change in the value of $y$ with respect to $x$ in the equation, i.e. $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$. The y intercept is the point at which the line cuts the y-axis which we can find by putting $x = 0$. Alternatively, we can find the slope of the line and the y-intercept simultaneously by using the slope-intercept formula wherein we write the given equation in the form $y = mx + c$, where $m$ is the slope of the line and $c$ is the y-intercept.

Complete step by step solution:
We have to find the slope and y intercept of the line given by the equation $3y = - 6x + 9$.
We will use the slope-intercept formula to find the slope of the line.
The slope-intercept formula is given by $y = mx + c$.
We can rewrite the given equation in the form,
$\Rightarrow 3y = - 6x + 9 \\\ \Rightarrow y = \dfrac{{ - 6x}}{3} + \dfrac{9}{3} \\\ \Rightarrow y = - 2x + 3 \\\$
On comparing with the standard form of the slope-intercept formula, we see that
$m = - 2$ and $c = 3$
Thus, the slope of the given line is $- 2$ and the y-intercept is $3$.
Hence, the slope of the line $3y = - 6x + 9$ is $- 2$ and it cuts the y-axis at the point $(0,{\kern 1pt} {\kern 1pt} {\kern 1pt} 3)$.

Thus, the slope of the given line is $- 2$ and the y-intercept is $3$.

Note: For a horizontal line parallel to x-axis, the slope is $0$ as the value of $y$ does not change for any change in the value of $x$. The y-intercept $4y = 20$ is $(0,{\kern 1pt} {\kern 1pt} {\kern 1pt} 5)$ as $y = 5$ for all values of $x$. We can also find the y intercept of the line by putting $x = 0$ in the equation as when the line is cutting the y-axis the value of $x$ is $0$.