Answer:
y = -1/3x + 1
Step-by-step explanation:
substitute the given values in y = mx + b where m is the slope and b is the y-intercept
y = -1/3x + b
at point (0, 1)
1 = -1/3 × 0 + b
1 = 0 + b
b = 1
y = -1/3 + 1
Answer: The required equation of the line is [tex]x+3y=3.[/tex]
Step-by-step explanation: We are given to find the equation of a line with slope [tex]-\dfrac{1}{3}[/tex] and y-intercept (0, 1).
We know that
the equation of a line with slope m and y-intercept (0, c) is given by
[tex]y=mx+c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
From the given information, we have
[tex]\textup{slope, }m=-\dfrac{1}{3},\\\\\textup{y-intercept, }(0,c)=(0,1)~~~\Rightarrow c=1.[/tex]
Therefore, from equation (i), we get
[tex]y=mx+c\\\\\Rightarrow y=-\dfrac{1}{3}x+1\\\\\Rightarrow 3y=-x+3\\\\\Rightarrow x+3y=3.[/tex]
Thus, the required equation of the line is [tex]x+3y=3.[/tex]
