3Y + 6x = 18
4y – 12x = -16
a.) Get each equation in slope-intercept form.
b.) Identify the slope and the y-intercept of each equation.
c.) Find the x and y-intercepts of each line.
from (a), (b) is trivial
y = -2x + 6
y = 3x - 4
intercepts:
(0,6) and (3,0)
(0,-4) and (4/3,0)
To solve this system of equations and answer the given questions, we can go through the following steps:
a) Get each equation in slope-intercept form:
To write an equation in slope-intercept form (y = mx + b), we need to isolate the variable y.
Equation 1: 3y + 6x = 18
Start by subtracting 6x from both sides:
3y = -6x + 18
Then, divide both sides by 3 to isolate y:
y = -2x + 6
Equation 2: 4y - 12x = -16
Start by adding 12x to both sides:
4y = 12x - 16
Then, divide both sides by 4 to isolate y:
y = 3x - 4
b) Identify the slope and the y-intercept of each equation:
In the slope-intercept form (y = mx + b), the coefficient of x (m) represents the slope of the line, while the constant term (b) represents the y-intercept.
For Equation 1: y = -2x + 6
Slope: The coefficient of x is -2, so the slope is -2.
Y-intercept: The constant term is 6, so the y-intercept is (0, 6).
For Equation 2: y = 3x - 4
Slope: The coefficient of x is 3, so the slope is 3.
Y-intercept: The constant term is -4, so the y-intercept is (0, -4).
c) Find the x and y-intercepts of each line:
To find the x-intercept, we can substitute y = 0 into the equation and solve for x. To find the y-intercept, we can substitute x = 0 into the equation and solve for y.
For Equation 1: y = -2x + 6
X-intercept: Substitute y = 0:
0 = -2x + 6
Rearrange and solve for x:
2x = 6
x = 3
So, the x-intercept is (3, 0).
Y-intercept: Substitute x = 0:
y = -2(0) + 6
y = 6
So, the y-intercept is (0, 6).
For Equation 2: y = 3x - 4
X-intercept: Substitute y = 0:
0 = 3x - 4
Rearrange and solve for x:
3x = 4
x = 4/3
So, the x-intercept is (4/3, 0).
Y-intercept: Substitute x = 0:
y = 3(0) - 4
y = -4
So, the y-intercept is (0, -4).
In summary:
Equation 1: Slope = -2, Y-intercept = (0, 6), X-intercept = (3, 0)
Equation 2: Slope = 3, Y-intercept = (0, -4), X-intercept = (4/3, 0)