Question

How do you charge $ 3x+y=15 $ into slope-intercept form?

Answer 1

Hint: We will look at the different forms of the equation of a line. We will also see the general equations of these different forms and the information required to construct these equations. We will see the slope-intercept form of the equation of the line and compare it to the given linear equation. Then we will rearrange the terms in the given equation to obtain it in the slope-intercept form.

Complete step by step answer:
There are multiple ways of writing a linear equation. The following are some of the different forms of the equation of a line:
(i) Slope point form.
We have a point $ \left( {{x}_{1}},{{y}_{1}} \right) $ and the slope of the line given by $ m $ . The equation of line in this form is given as $ y-{{y}_{1}}=m\left( x-{{x}_{1}} \right) $ .
(ii) Slope intercept form.
We have the slope of the line given by $ m $ and the y-intercept $ \left( 0,b \right) $ . The equation of line is then given as $ y=mx+b $ .
(iii) Two-point form.
We have two points $ \left( {{x}_{1}},{{y}_{1}} \right) $ and $ \left( {{x}_{2}},{{y}_{2}} \right) $ . Then the equation of line is given by $ y-{{y}_{1}}=\left( {{y}_{2}}-{{y}_{1}} \right)\times \dfrac{x-{{x}_{1}}}{{{x}_{2}}-{{x}_{1}}} $ .
(iv) Intercept form.
We have the x-intercept as $ \left( a,0 \right) $ and y-intercept as $ \left( 0,b \right) $ . The equation of line in this form is given as $ \dfrac{x}{a}+\dfrac{y}{b}=1 $ .
The equation of a line in slope-intercept form is given as $ y=mx+b $ . The given linear equation is $ 3x+y=15 $ . To make the given equation into the slope-intercept form, we will shift the constant term and the variable $ x $ term to one side. We get the following equation,
 $ y=-3x+15 $
Comparing the above equation to the general slope-intercept form equation, we can see that $ m=-3 $ and $ b=15 $ . So, the slope-intercept form of the given equation is $ y=-3x+15 $ .

Note:
The graph of the given equation looks like the following,

We can use the graph to find the slope using the coordinates of two points. We can also see the y-intercept from the graph. So, instead of rearranging the given equation, we can find the needed parts from the graph and construct the slope-intercept form of the equation.