You were given standard form for both lines. It is your call, but I would avoid transforming any of the equations to slope intercept form. I would also answer with the same equation form used in the question.
For the y-intercept of the second equation substitute x = 0.
-(0) - 2y = 4
y = -2
y-intercept: (0, -2)
For a line perpendicular to the first line, transpose the coefficients of x and y, and change the sign of one of them.
9x + 5y → 5x - 9y
Complete the equation by evaluating it at (0, -2).
-2x - 2y = 4 becomes x + y = -2 if you divide everywhere by -2, and in turn that becomes y = -x - 2 in slope-intercept. The y intercept is (0, -2).
A line perpendicular to 9x + 5y = -3 must have a negative reciprocal slope of this line; here, it would need to be 5/9, as the aforementioned line has a slope of -9/5 (put that in slope-intercept and you'll see this is the case).
You can now use point-slope.
y - (-2) = (5/9)(x - 0)
y + 2 = (5/9)x
y = (5/9)x - 2 in slope-intercept. In standard form: 5x - 9y = 18. Final.
Answers & Comments
The typical equation of a line is: y = mx + b → where m: slope and where b: y-intercept
9x + 5y = - 3 ← this is the line (ℓ₁)
5y = - 9x - 3
y = (- 9x - 3)/5
y = - (9/5).x - (3/5) ← the slope is (- 9/5)
- 2x - 2y = 4 ← this is the line (ℓ₂)
- 2y = 2x + 4
2y = - 2x - 4
y = (- 2x - 4)/2
y = - (2/2).x - (4/2)
y = - x - 2 ← the y-intercept is (- 2)
Two lines are perpendicular if the product of their slope is - 1.
As the slope of the line (ℓ₁) is (- 9/5), the slope of the line (ℓ₃) is (5/9).
The equation of the line (ℓ₃) becomes: y = (5/9).x + b
The y-intercept of the line (ℓ₃) is the same as the line (ℓ₂), i.e. (- 2), so the equation of the line (ℓ₃) is:
y = (5/9).x - 2
Find an equation for the line perpendicular to the line 9x+5y=−3 having the same y-intercept as −2x−2y=4.
Find an equation for the line perpendicular to the line 9x+5y=−3 having the same y-intercept as x/(-2)+y/(-2)=1.
Find an equation for the line perpendicular to the line 9x+5y=−3 that passes through (0,-2).
5x-9y=5*0-9*-2 simplifies to 9x + 5y = 18 which is an equation of the sought line, using the same form as the two lines given in the question.
You were given standard form for both lines. It is your call, but I would avoid transforming any of the equations to slope intercept form. I would also answer with the same equation form used in the question.
For the y-intercept of the second equation substitute x = 0.
-(0) - 2y = 4
y = -2
y-intercept: (0, -2)
For a line perpendicular to the first line, transpose the coefficients of x and y, and change the sign of one of them.
9x + 5y → 5x - 9y
Complete the equation by evaluating it at (0, -2).
5x - 9y = 5(0) - 9(-2)
5x - 9y = 18
9x + 5y = -3
y = -9x/5 -3/5....[1]
-2x -2y = 4
y = -x/2 -2....[2]
Ans: y = 5x/9 - 2
-2x - 2y = 4 becomes x + y = -2 if you divide everywhere by -2, and in turn that becomes y = -x - 2 in slope-intercept. The y intercept is (0, -2).
A line perpendicular to 9x + 5y = -3 must have a negative reciprocal slope of this line; here, it would need to be 5/9, as the aforementioned line has a slope of -9/5 (put that in slope-intercept and you'll see this is the case).
You can now use point-slope.
y - (-2) = (5/9)(x - 0)
y + 2 = (5/9)x
y = (5/9)x - 2 in slope-intercept. In standard form: 5x - 9y = 18. Final.
Y-intercept of -2x - 2y = 4 can be found by setting x to 0. The y-intercept is therefore -2.
9x + 5y = -3
5y = -9x - 3
y = -9/5 (x) - 3
Slope of this line is -9/5. Slope of perpendicular line is 5/9.
Answer: y = (5/9)x - 2