Respuesta :
Answer:
y = (-1/3)x + 4
Explanation:
The slope-intercept form of a line can be calculated as:
[tex]y=m(x_{}-x_1)+y_1_{}[/tex]Where (x1, y1) is a point in the line and m is the slope.
On the other hand, two lines are perpendicular if the product of their slopes is equal to -1. It means that the slope of a line that is perpendicular to y = 3x + 1 can be calculated as:
[tex]\begin{gathered} 3\cdot m=-1 \\ \frac{3\cdot m}{3}=-\frac{1}{3} \\ m=-\frac{1}{3} \end{gathered}[/tex]Because the slope of the line y = 3x + 1 is 3.
Then, replacing m by -1/3 and (x1, y1) by (-3, 5), we get that equation of the line is:
[tex]\begin{gathered} y=-\frac{1}{3}(x-(-3))+5 \\ y=-\frac{1}{3}(x+3)+5 \end{gathered}[/tex]Finally, applying the distributive property, we get:
[tex]\begin{gathered} y=-\frac{1}{3}x-\frac{1}{3}\cdot3+5 \\ y=-\frac{1}{3}x-1+5 \\ y=-\frac{1}{3}x+4 \end{gathered}[/tex]Therefore, the slope-intercept form of the line is: y = (-1/3)x + 4
