Answer:
[tex]y = \frac{1}{3}x + 5[/tex]
Step-by-step explanation:
By definition, two lines are perpendicular if and only if their slopes are negative reciprocals of each other: [tex]m = - \frac{1}{m_{2} }[/tex], or equivalently, [tex]m_{1} * m_{2} = -1[/tex].
Given our linear equation 3x + y = 3 (or y = -3x + 3):
We can find the equation of the line (with a y-intercept of 5) that is perpendicular to y = -3x + 3 by determining the negative reciprocal of its slope, -3, which is [tex]\frac{1}{3}[/tex].
To test whether this is correct, we can take first slope, [tex]m_{1} = -3[/tex], and multiply it with the negative reciprocal slope [tex]m_{2} = \frac{1}{3}[/tex] :
[tex]m_{1} * m_{2} = -1[/tex]
[tex]-3 * \frac{1}{3} = -1[/tex]
Therefore, we came up with the correct slope for the other line, which is [tex]\frac{1}{3}[/tex].
Finally, the y-intercept is given by (0, 5). Therefore, the equation of the line that is perpendicular to 3x + y = 3 is:
[tex]y = \frac{1}{3}x + 5[/tex]
