Question
write the following equation in slope intercept form y>|5-x|+1
Answers
GPT 3.5
To write the equation in slope-intercept form, we need to isolate y on one side of the equation.
Given: y > |5 - x| + 1
First, let's remove the absolute value sign by considering the two cases when the expression inside the absolute value is positive and negative:
Case 1: (5 - x) ≥ 0
In this case, we can rewrite the equation as:
y > 5 - x + 1
Simplifying this, we have:
y > 6 - x
Case 2: (5 - x) < 0
In this case, we need to flip the sign when removing the absolute value, so the equation becomes:
y > -(5 - x) + 1
Simplifying this, we have:
y > -5 + x + 1
Combining both cases, the equation can be written as:
y > 6 - x or y > -4 + x
Now, let's write it in slope-intercept form by rearranging the terms:
y > -x + 6 or y > x - 4
These equations are the slope-intercept form of y > |5 - x| + 1.
Given: y > |5 - x| + 1
First, let's remove the absolute value sign by considering the two cases when the expression inside the absolute value is positive and negative:
Case 1: (5 - x) ≥ 0
In this case, we can rewrite the equation as:
y > 5 - x + 1
Simplifying this, we have:
y > 6 - x
Case 2: (5 - x) < 0
In this case, we need to flip the sign when removing the absolute value, so the equation becomes:
y > -(5 - x) + 1
Simplifying this, we have:
y > -5 + x + 1
Combining both cases, the equation can be written as:
y > 6 - x or y > -4 + x
Now, let's write it in slope-intercept form by rearranging the terms:
y > -x + 6 or y > x - 4
These equations are the slope-intercept form of y > |5 - x| + 1.