Question

How do you write an equation in point slope form when the slope is \[\dfrac{1}{3}\] and the y-intercept is -4.

Answer 1

Hint:In this problem, we have to find an equation in point slope form. We are given a slope and y-intercept. We know that the equation of point slope form is \[\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)\]. Here we have to substitute the slope value and a point, where we have only slope. But we are given y-intercept, we know that at y-intercept the value of x is 0, therefore, we will get a point to be substituted in the formula to get an equation.

Complete step by step answer:
We know that the equation of point slope form is,
 \[\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)\]……. (1)
Where, m is the slope and \[\left( x,y \right)\] is the point.
We are given the slope, m = \[\dfrac{1}{3}\] and y-intercept, c = -4.
But here, we need a point to be substituted to get an equation.
We know that, at y-intercept the value of x is 0, i.e. x = 0.
Hence, we can get a point, \[\left( x,y \right)=\left( 0,-4 \right)\].
We can now substitute the above point and the slope value in the point slope formula (1), we get
\[\Rightarrow \left( y+4 \right)=\dfrac{1}{3}x\]
Therefore, the required equation is \[\left( y+4 \right)=\dfrac{1}{3}x\].

Note: We should know that the formula for the equation of slope point form is \[\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)\], where we should have a slope and a point to find the required equation. We may not be given a direct value to be substituted instead we should find the data required for the equation from the given data.