Answer:
The equation in slope-intercept form of the line perpendicular to y = -3x + 1 and passing through (2, 2) is y = (1/3)x + 4/3.
Explanation:
To find the equation of the line perpendicular to y = -3x + 1 and passing through the point (2, 2), we first need to determine the slope of the line we are looking for.
The slope of any line perpendicular to y = -3x + 1 will be the negative reciprocal of the slope of y = -3x + 1. The slope of y = -3x + 1 is -3, so the slope of the line we want is the negative reciprocal of -3, which is 1/3.
So the slope of the line we want is 1/3. We also know that the line passes through the point (2, 2). We can now use the point-slope form of the equation of a line to find the equation of the line we want:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is the point the line passes through.
Substituting m = 1/3, x1 = 2, and y1 = 2, we get:
y - 2 = (1/3)(x - 2)
Multiplying both sides by 3, we get:
3y - 6 = x - 2
Subtracting x from both sides, we get:
-x + 3y = 4
So the equation of the line perpendicular to y = -3x + 1 and passing through the point (2, 2) is -x + 3y = 4, which is in standard form. We can also write it in slope-intercept form:
3y = x + 4
y = (1/3)x + 4/3
So the equation of the line we want in slope-intercept form is y = (1/3)x + 4/3.
Hope this helps you! Sorry if it doesn't. If you need more help, ask me! :]