What is an equation of the line, in point-slope form, that passes through the given point and has the given slope?
a. y-9=4/9(x+3)
b. y-9+4/9(x-3)
c. y+3=4/9(x-9)
d. y-3=4/9(x-9)
To find the equation of a line in point-slope form, you need the slope of the line and a point that it passes through.
Let's analyze each option:
a. y-9=4/9(x+3)
This equation is in point-slope form, where the given point is (-3, 9), and the slope of the line is 4/9. Therefore, option a is correct.
b. y-9+4/9(x-3)
This equation is not in point-slope form. The point is (3, 9), but the equation does not match the correct format. Option b is incorrect.
c. y+3=4/9(x-9)
This equation is not in point-slope form. The point is (9, -3), but the equation does not match the correct format. Option c is incorrect.
d. y-3=4/9(x-9)
This equation is in point-slope form, where the given point is (9, 3), and the slope of the line is 4/9. Therefore, option d is correct.
So, the equation of the line in point-slope form that passes through the given point and has the given slope is either option a or option d.