Perpendicular lines have a slope that is the opposite reciprocal of the original line slope. To find it, first flip the fraction (-3 to -1/3). Then, add/get rid of the negative sign based on if it was there in the first place (-1/3 to 1/3). Thus, the slope would be 1/3.
y = -2
x = 3
Step-by-step explanation:
Solve using elimination
1. Rearrange the equations to make it easier to solve
y = -3x + 7 → 3x + y = 7
y = 2x - 8 → 2x - y = 8
2. Multiply the equations to have a matching coefficient
2(3x + y = 7) = 6x + 2y = 14
3(2x - y = 8) = 6x - 3y = 24
3. Subtract
6x + 2y = 14
- 6x - 3y = 24
0 + 5y = -10
4. Solve for y
5y = -10
y = -2
5. Substitute y in any equation to solve for x
-2 = -3x + 7
-3x = -9
x = 3
x = 3, y = -2
Step-by-step explanation:
Since y=y
then, -3x +7 = 2x-8
7+8 = 3x+2x
15 = 5x
x=3
substitute
y = 2(3) - 8
y = -2
Hope that helped!!! k
1) y = -8/5x + 8
2) slope = -3
3) x = 4
4) x ≥ 22/3
5) x = 21/16
6) x = 12
Step-by-step explanation:
1) For the slope, you know you go up 8 left 5 to get from the x-intercept to your y-intercept so it’s positive 8 over -5 (rise over run).
This makes your slope 8/-5 which is the same as -8/5
2) The slope is next to the x, so the slope is -3/1 which is -3.
3) Rearrange the equation to y = mx + b.
Firstly, subtract 6x from both sides:
-3y = -6x + 24
Then, divide both sides by -3:
y = 2x - 8
To get the x-intercept, divide the y-intercept (but positive) by the slope.
8/2 = 4
Your x-intercept is 4.
4) Distribute on the terms:
-53 ≥ -9x - 9 + 3x
Combine like terms:
-53 ≥ -6x - 9
Add 9 to both sides:
-44 ≥ -6x
Divide both sides by -6:
44/6 ≤ x
(Inequality flipped because you divide by a negative)
Simplify:
22/3 ≤ x
Flip the inequality:
x ≥ 22/3
5) Multiply both sides by 4:
3x - x/3 = 7/2
Multiply both sides by 3:
9x - x = 21/2
Combine like terms:
8x = 21/2
Divide both sides by 8:
x = 21/16
or
x = 1.3125
6) Combine like terms:
7x + 6 = 90
Subtract 6 from both sides:
7x = 84
Divide both sides by 7:
x = 12
Hope this helps!
D
Step-by-step explanation:
Slope is 'm' in y = mx + c
m is the coefficient of x
So, m = -3
(4, -5)
Step-by-step explanation:
we know that
If a ordered pair lie on the line, then the ordered pair must satisfy the equation of the line
we have
[tex]y=-3x+7[/tex]
Verify each ordered pair
case 1) (4, -5)
substitute the value of x and the value of y in the linear equation and then compare the results
[tex]-5=-3(4)+7[/tex]
[tex]-5=-5[/tex] ---> is true
so
The ordered pair satisfy the linear equation
therefore'
The ordered pair lie on the line
case 2) (4, 19)
substitute the value of x and the value of y in the linear equation and then compare the results
[tex]19=-3(4)+7[/tex]
[tex]19=-5[/tex] ---> is not true
so
The ordered pair not satisfy the linear equation
therefore'
The ordered pair not lie on the line
case 3) (1,5)
substitute the value of x and the value of y in the linear equation and then compare the results
[tex]5=-3(1)+7[/tex]
[tex]5=4[/tex] ---> is not true
so
The ordered pair not satisfy the linear equation
therefore'
The ordered pair not lie on the line
case 4) (1,-19)
substitute the value of x and the value of y in the linear equation and then compare the results
[tex]-19=-3(1)+7[/tex]
[tex]-19=4[/tex] ---> is not true
so
The ordered pair not satisfy the linear equation
therefore'
The ordered pair not lie on the line
1/3
Step-by-step explanation:
Perpendicular lines have a slope that is the opposite reciprocal of the original line slope. To find it, first flip the fraction (-3 to -1/3). Then, add/get rid of the negative sign based on if it was there in the first place (-1/3 to 1/3). Thus, the slope would be 1/3.
Hope this helped 🙂
d
Step-by-step explanation:
1.（A）Ithink it is the option a, because b,c,d cannot be equaled to that equation
-3
Step-by-step explanation:
the coefficient of the x term is the slope in any equation that is in slope intercept form
The equation that represents the other equation is [tex]y=\dfrac{1}{3}x+5[/tex] .
The solution of the system is (3,6).
Step-by-step explanation:
Linear equation: [tex]y=mx+c[/tex] , where m= slope
c = y-intercept.
In the first table, the y-intercept = 5 [ y-intercept = value of y at x=0.
Slope for first table = [tex]\dfrac{y_2-y_2}{x_2-x_1}=\dfrac{6-5}{3-0}=\dfrac{1}{3}[/tex]
The equation that represents the first table:
[tex]y=\dfrac{1}{3}x+5[/tex]
So, the equation that represents the other equation is [tex]y=\dfrac{1}{3}x+5[/tex] .
Also, the solution of the system is the common point (x,y) that satisfy both equations in the system.
Here, x=3 and y=6 is the common value in both tables.
So, the solution of the system is (3,6).