Question

How do you find the slope and intercept of $ 3x+y=6 $ ?

Answer 1

Hint: In this question, we have to find the slope and intercept of the equation. Thus, we use the slope-intercept form. As we know that, the slope is the ratio of the vertical change or horizontal change between any two distinct points on the curve. About intercepts, the x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. Thus, we transform the equation into the line of the equation $ y=mx+c $ , by subtracting 3x on both sides of the equation, to get the transformed equation. Thus, we compare the general line of the equation and transformed equation, to get the value of slope and intercepts of the equation, which is our required answer

Complete step by step answer:
In this question, we have to plot the equation $ 3x+y=6 $ using slope-intercept form.
As we know, the equation of the line is $ y=mx+c $ , where
m is the slope of the equation = $ \dfrac{y}{x}=\dfrac{\text{rise}}{\text{run}} $ , means y will go vertically and x will go horizontal
In addition, c is the y-intercept =constant ------------- (1)
Therefore, we rearrange the equation $ 3x+y=6 $ in the form of $ y=mx+c $ , that is
Equation: $ 3x+y=6 $ ---------- (2)
We will subtract 3x on both sides of the equation (2), we get
 $ 3x+y-3x=6-3x $
As we know, the same terms will cancel out with opposite signs, we get
 $ y=6-3x $
Therefore, we get
 $ y=-3x+6 $ ------------- (3)
As we see the above equation has transformed into the equation $ y=mx+c $ .
Therefore, on comparing equations (1) and (3), we get that
The slope of the equation $ 3x+y=6 $ = $ m=-3 $ , and
The intercept of y-axis $ 3x+y=6 $ = $ c=6 $ .
Thus, for the equation $ 3x+y=6 $ slope $ m=-3 $ and y-intercept $ c=6 $ or $ c=\left( 0,6 \right) $.

Note:
Always do proper calculations to get the exact slope and intercept of the equation. One of the alternative methods to solve this problem is you can also find the y-intercept by using the substitution method. Let x=0 in the equation and solve for y, which is the required y-intercept for the answer.