Write an equation of the line that passes through
(3, 5) and is perpendicular to the graph of y = –3x
+7. Write your final equation in slope-intercept
form.
The equation of the line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Given that the line is perpendicular to the graph of y = -3x + 7, we know that the slope of the line we are looking for is the negative reciprocal of -3.
The slope of the line we are looking for is 1/3.
We know that the line passes through (3, 5). We can use this information to find the y-intercept.
Using the slope-intercept form of a line, we can substitute the slope (1/3), the x-coordinate (3), and the y-coordinate (5) into the equation to find the y-intercept:
5 = (1/3)(3) + b
5 = 1 + b
b = 5 - 1
b = 4
Therefore, the final equation of the line that passes through (3, 5) and is perpendicular to the graph of y = -3x + 7 is:
y = (1/3)x + 4