Question

How do you write an equation in slope intercept form given, $m=-\dfrac{2}{3},b=5$.

Answer 1

In this problem, we have to write an equation in slope intercept form. We are given a slope, m value and an intercept, b value. We know that the slope intercept form is, $y=mx+b$. We know that we are already given the slope value and an intercept value, which we have to substitute in the slope-intercept formula to find the equation of the line.

Complete step by step answer:
We know that the slope intercept form of the line is,
$y=mx+b$ ……. (1)
Where, m is the slope and b is the y-intercept.
We know that, we are given $m=-\dfrac{2}{3},b=5$
We can substitute the above slope, m value and y-intercept value in the slope intercept equation (1), we get
$\Rightarrow y=\dfrac{-2}{3}x+5$
We can now simplify the above step.
We can cross multiply the right-hand side part, we get
$\Rightarrow y=\dfrac{-2x+15}{3}$
We can now divide by number 3 on both the left-hand side and the right-hand side of the equation and simplify the step by cancelling similar terms, we get
$\Rightarrow 3y=-2x+15$
Therefore, the required equation is $2x+3y=15$.

Note: We should know the equation of the slope intercept form is $y=mx+c$, where m is the slope and c is the y-intercept. Here we have a slope value, so we can directly substitute it in the formula, but if two points are given, we can use the slope formula of two points to find the slope value and to substitute in the equation.