Question

How do you find the slope and the y-intercept for $ y=6x+4 $ .

Answer 1

Hint:
 The above-given question is of linear equation in one variable. Since, we know that the slope-intercept form of the line equation is given as y = mx + c, where m is the slope of the line and c is the y-intercept. In the given equation $ y=6x+4 $ , we have m = 6 and $ c=4 $ . So, we will say that the line $ y=6x+4 $ has a slope equal to 6 and t-intercept equal to 4.

Complete step by step answer:
We know that the above question is of linear equation in one variable.
We also know that the slope-intercept form of the linear equation is given y = mx + c, where m is the slope of the line and c is the y-intercept. The slope is the tangent of the angle made by the line with the x-axis and the y-intercept is the point at which the line cuts the y-axis.
Now, we will compare the equation $ y=6x+4 $ with general equation y = mx + c.
After comparing we will get: m = 6 and $ c=4 $ .
So, the slope of the line $ y=6x+4 $ is equal to 4, and the and the y-intercept is equal to 4 .
We can plot the graph of the line $ y=6x+4 $ as:

This is our required solution.

Note:
Student are required to note that when we have general equation of the line as \[ax+by+c=0\], then slope of the line is equal to $ -\dfrac{a}{b} $ and y-intercept is equal to $ -\dfrac{c}{a} $ . WE can also find the slope of the line by equating the first derivative of the line equation to 0 i.e. $ \dfrac{dy}{dx}=0 $ and when we put x = 0, we will get the y-intercept of the line.