Question

What is the slope of the line whose equation is \[3x-y=4\]?

Answer 1

Hint: We know that slope is the ratio of changes in the y values to the changes in the x values. We can find slope value in two methods, that is we can find through the graph and another is we can find through the line equation. In this problem the equation of line is given, which is of the form of slope-intercept form. The slope intercept form is of the form \[y=mx+b\], where m is the slope value and b is the y-intercept. Comparing the slope intercept form and the given equation, we can find the slope value.

Complete step-by-step answer:
We know that,
The equation of a line with slope m and making an intercept b on Y-axis, is
\[y=mx+b\]…….. (1)
Here, we can see m is the slope.
We also know that the given equation of line is of the form
\[y=3x-4\]……. (2)
Now we can compare the slope-intercept form and the given equation.
Comparing equation (1) and (2), we get
\[y=mx+b\]
\[y=3x-4\]
Here comparing the above two equations, the coefficient of x in both the equations are m and 3
The value of m is 3.
Therefore, the slope value, m = 3.

Note: Students may make mistakes, when the line equation is not in the exact slope intercept form, in that case, we get confused in finding the value of slope. Here we have to know that the coefficient of x is the slope value and the constant value is the y-intercept.