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

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.