Question

How do you find the slope and intercept of \[y=-\dfrac{2}{5}x+20\]?

Answer 1

Hint: 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 \[-\dfrac{2}{5}\] and the intercept c of the given equation is equal 20.

Complete step-by-step solution:
According to the question, we are asked to find the slope and intercept of the equation \[y=-\dfrac{2}{5}x+20\].
We have been given the equation is \[y=-\dfrac{2}{5}x+20\]. -----(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 \[-\dfrac{2}{5}\] and in the slope-intercept form, the coefficient of x is m.
Since equation (1) is of slope intercept form, we get
\[m=-\dfrac{2}{5}\]
Therefore, the slope of the equation (1) is \[-\dfrac{2}{5}\].
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 20 is the constant.
Comparing with the slope-intercept form of a line equation, we get
c=20.
Therefore, the intercept of the equation (1) is 20.
Hence, the slope and intercept of the equation \[y=-\dfrac{2}{5}x+20\] are \[-\dfrac{2}{5}\] and 20 respectively.

Note: We should not get confused with the slope-intercept form and point-intercept form. Here, we are asked to find the intercept of the equation which means ‘c’ in the slope-intercept form and not x and y intercepts individually. Also avoid calculation mistakes based on sign conventions.