Question

How do you find slope, y-intercept, x-intercept of $y = 3x$?

Answer 1

For the given problem we will use the straight-line equation formula which is $y = mx + c$. Slope-intercept form can be stated as the other name for the above equation. By comparing, the equation with the given straight-line equation. And, then by simplifying you will get the required slope and intercept.

Complete step by step solution:
We have to solve the given equation $y = 3x$.
From the slope-intercept formula $y = mx + c$, we can determine the solution by comparing with the given equation. Here, m is the slope which is given as 3. And y-intercept that is c is 0 because we have no constant added to the term x in our problem.
To find the x-intercept, we have to substitute y as 0 and then solve it to find x:
$\Rightarrow 0 = 3x$ [where y=0]
We can re-write the above equation, we get,
$\Rightarrow 3x = 0$
Dividing both sides by 3 and cancel all the common factors, we get,
$\Rightarrow \dfrac{{3x}}{3} = \dfrac{0}{3}$
Now, simplify the above equation, we get,
$\Rightarrow x = 0$

Therefore, the slope is 3 and x and the y-intercept is 0.

Additional Information:
The equation of the straight line is $ax + by + c = 0$, where x, y are variables and a, b, c are constants. The slope can also be determined with the help of $tan\theta$. Straight line general or standard form is $y = mx + c$. And the slope-point form or the equation of a line with two points is $(y - {y_1}) = m(x - {x_1})$

Note:
$y = mx + c$is the generally straight-line equation, where m is slope or gradient, and y = c that is the value where the line cuts the y-axis. The c is intercepted on the y-axis. The equation of the line in the intercept form is $\dfrac{x}{a} + \dfrac{y}{b} = 1$ where a is the x-intercept and b is the y-intercept.