5. Find the x and y intercepts of each linear equation. Be sure to write your answers as ordered pairs.
y = 3x - 6
6y = -x + 2
On the second equation, change it to read y= ...,. Divide both sides of that equation by 6 to get the desired result.
how??
The first one has slope m=3 and y intercept of -6.
To find the x intercept set y=0 and solve for x to get
0 = 3x - 6 or 6=3x and x=2
The second equation is
6y=-x+2
Divide both sides by 6 to get
y = (-1/6)x + 1/3
The y intercept is 1/3
To find the x intercept set y=0 and solve for x
0=(-1/6)x + 1/3 or
-1/3 = (-1/6)x multiply both sides by -6 to get
-6 * -1/3 = x or x=2
To find the x-intercept, you need to set the value of y to zero in the equation and solve for x.
For the first equation, y = 3x - 6, set y = 0:
0 = 3x - 6
To isolate x, add 6 to both sides:
6 = 3x
Divide both sides by 3:
2 = x
So the x-intercept of the first equation is 2.
To find the y-intercept, you need to set the value of x to zero in the equation and solve for y.
For the first equation, substitute x = 0:
y = 3(0) - 6
y = -6
So the y-intercept of the first equation is -6.
Now, let's tackle the second equation. To make it easier to work with, convert it to y = ... form by dividing both sides by 6:
6y = -x + 2
Divide both sides by 6:
y = (-1/6)x + 1/3
To find the y-intercept, set x = 0:
y = (-1/6)(0) + 1/3
y = 1/3
So the y-intercept of the second equation is 1/3.
To find the x-intercept, set y = 0:
0 = (-1/6)x + 1/3
Multiply both sides by -6 to get rid of the fraction:
0 = x/6 - 2/6
0 = x/6 - 1/3
Simplify:
0 = x/6 - 2/6
0 = (x - 2)/6
To isolate x, multiply both sides by 6:
0 = x - 2
Add 2 to both sides:
2 = x
So the x-intercept of the second equation is 2.
Therefore, the x-intercepts and y-intercepts of each linear equation are as follows:
First equation: x-intercept = (2, 0), y-intercept = (0, -6)
Second equation: x-intercept = (2, 0), y-intercept = (0, 1/3)