Answer:
y = 1/3x - 2:
- y - intercept: - 2
- x - intercept: 6
y = 12 - 6x:
- y - intercept: 12
- x - intercept: 2
y = 3x - 7:
- y - intercept: -7
- x - intercept: 7/3
Step-by-step explanation:
Hello!
Slope Intercept Form
The slope-intercept form of a line is [tex]y = mx + b[/tex]
- y = output, ordinate
- m = slope
- x = input, abscissa
- b = y-intercept
y = 1/3x - 2
The y-intercept is the "b" value of the line, given as -2.
To find the x-intercept, we simply replace the y-value with 0:
- 0 = 1/3x - 2
- 2 = 1/3x
- 6 = x
y - intercept: - 2
x - intercept: 6
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y = 12 - 6x
You can rearrange the equation, y = -6x + 12, to find the y-intercept: 12.
Solving for the x-intercept (remember, replace y with 0):
- 0 = -6x + 12
- -12 = -6x
- 2 = x
y - intercept: 12
x - intercept: 2
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y = 3x - 7
Simply take the "b" value, -7, to find the y-intercept of -7.
Solve for the x-intercept:
y - intercept: -7
x - intercept: 7/3
Additional Note:
You can also solve for the y-intercept by replacing x with 0. This method can be used for any interests, just plug in the opposite variable from what you are solving for with 0.
The proof is that the x-intercept is the value when the y = 0, the x-axis. You can plug in 0 for y to solve for x. Similarly, when solving for the y-intercept, you plug 0 for x as the y-axis is at x = 0.
