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Question: How do you find the slope and intercept of \[y=3x-1\]?...

How do you find the slope and intercept of y=3x−1y=3x-1?

Explanation

Solution

This type of problem is based on the concept of equation of line. First, we have to consider the given equation. Compare the given equation with slope-intercept form of an equation, that is y=mx+c, where m is the slope of the equation and c is the intercept of the equation. Here, the given equation is also in the slope-intercept form where the slope m of the given equation is equal to 3 and the intercept c of the given equation is equal -1.

Complete step-by-step solution:
According to the question, we are asked to find the slope and intercept of the equation y=3x−1y=3x-1.
We have been given the equation is y=3x−1y=3x-1. -----(1)
Consider the given equation first.
We know that the slope intercept form of a line equation is y=mx+c.
Where m is the slope of the equation and c is the intercept of the equation.
Compare the given equation (1) with slope-intercept form.
We find that the considered equation (1) is also in the slope intercept form.
In equation (1), the coefficient of x is 3 and in the slope-intercept form, the coefficient of x is m.
Since equation (1) is of slope intercept form, we get
m=3
Therefore, the slope of the equation (1) is 3.
Now, we need to find the intercept.
In the standard slope-intercept form y=mx+c, c is the intercept.
In equation (1) we find that -1 is the constant.
Comparing with the slope-intercept form of a line equation, we get
c=-1.
Therefore, the intercept of the equation (1) is -1.
Hence, the slope and intercept of the equation y=3x−1y=3x-1 are 3 and -1 respectively.

Note: We should not get confused with the slope-intercept form and point-intercept form. Also avoid calculation mistakes based on sign conventions. Here, we are asked to find the intercept of the equation which means ‘c’ in the slope-intercept. We should not find the x and y intercepts instead. Always convert the given equation in such a manner that the y coordinate is on the left-hand side and the x coordinate with the constant is on the right-hand side of the equation.