Question

The equation of a line is X+3Y=14 what is the y-intercept of the line?

Answer 1

Answer:  The required y-intercept of the given line is $\dfrac{14}{3}.$  

Step-by-step explanation:  We are given to find the y-intercept of the following equation of a line :

$x+3y=14~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

The slope-intercept form of the equation of a line is given by

$y=mx+c,$ where m is the slope and c is the y-intercept of the line.

From equation (i), we have

$x+3y=14\\\\\Rightarrow 3y=-x+14\\\\\Rightarrow y=-\dfrac{1}{3}x+\dfrac{14}{3}.$

Comparing the above equation with the slope-intercept form, we get

$\textup{y-intercept, c}=\dfrac{14}{3}.$

Thus, the required y-intercept of the given line is $\dfrac{14}{3}.$  

Answer 2

X+3y=14
-x. -x
3y=-x+14
Divide them all by 3
Y=-x/3+14/3
Y-intercept= 1/3