Question

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

Answer 1

Hint: 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,
 $\Rightarrow {\displaystyle \frac{3x}{3}}={\displaystyle \frac{0}{3}}$
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 ${\displaystyle \frac{x}{a}}+{\displaystyle \frac{y}{b}}=1$ where a is the x-intercept and b is the y-intercept.