Question

How do you find the slope and intercept for $y = 4x$ ?

Answer 1

We know the equation of a line passing through a point and having a slope ‘m’ and with ‘y’ intercept as ‘c’ is given by $y = mx + c$ . Here, x and y are variables. We convert the given equation to the slope intercept form. Then comparing the simplified equation with the equation of slope intercept will give us the desired result that is the slope and intercept of the line whose equation is given to us.

Complete step by step solution:
In the given problem, we are required to find the slope and intercept of the line whose equation is given to us as $y = 4x$ .
The slope intercept form of the equation of a line is $y = mx + c$ where slope of line is given by ‘m’ and y-intercept is given by ‘c’.
So, $y = 4x$
So, firstly we have to shift the term consisting y to the left side of the equation. But, the term involving y is already on the left side of the equation. So, we have,
$\Rightarrow y = 4x$
So, the equation of the line given to us is already in the slope and intercept form of the line. Hence, we can directly start comparing the equation of the given line with the slope and intercept form of a line and get the values of slope and intercept of the line.
Therefore, on comparing the equation of the line given to us and the slope intercept form $y = mx + c$ of the line, we get,

Slope of the line $= m = 4$ and y-intercept $= c = 0$ .

Note: ‘y’ intercept is defined as the point where a line or a curve crosses the y-axis of a graph. In other words the value of ‘y’ at ‘x’ is equal to zero is called the y-intercept of the graph. Hence, the y intercept of a line can also be found by putting the value of x as zero. Slope of a line is the inclination of that straight line from the positive x-axis.