9. 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.
To find the equation of a line that is perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line.
The given line has a slope of -3, so the perpendicular line will have a slope that is the negative reciprocal of -3, which is 1/3.
The equation of the line passing through (3, 5) with a slope of 1/3 can be written in slope-intercept form as y = mx + b, where m represents the slope and b represents the y-intercept.
So, substituting the values m = 1/3 and (x, y) = (3, 5) into the equation, we have:
5 = (1/3) * 3 + b
Simplifying the equation:
5 = 1 + b
Subtracting 1 from both sides:
b = 5 - 1
b = 4
Therefore, the 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.