Answer:
- y = 2x -6
- y = -x +2
- y = 4/5x -2
- y = -3/2x +4
Step-by-step explanation:
The slope-intercept form of the equation for a line is ...
y = mx +b . . . . . where m is the slope, and b is the y-intercept
For these equations, writing them in slope-intercept form means "solve for y." You always do any "solve for ..." problem by undoing the operations that are done to the variable. Addition is undone by adding the opposite. Multiplication is undone by division.
As always, whatever operation we perform on one side of the equal sign must also be performed on the other side. That is how the equal sign remains valid.
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<h3>a)</h3>
1/2y = x -3
All we need to do is get rid of the coefficient of y. We can do that by dividing by 1/2, or multiplying by 2. The latter is easier to see, perhaps.
2(1/2y) = 2(x -3)
y = 2x +2(-3)
y = 2x -6
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<h3>b)</h3>
x +y = 2
Here, we need to undo the addition of x. We do that by adding (-x) to both sides of the equation.
-x +x +y = -x +2
y = -x +2
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<h3>c)</h3>
4x -5y -10 = 0
This is a combination of the above operations. We can separate the y-term from the others by either subtracting the others, or adding the opposite of the y-term. We choose the latter, because that will give a positive coefficient for y. Adding 5y to both sides gives ...
4x -5y +5y -10 = 5y
5y = 4x -10 . . . . . . . . simplify and put y on the left
Now, we need to divide by the coefficient of y. We do that to both sides of the equation.
5y/5 = (4x -10)/5
y = 4/5x -10/5
y = 4/5x -2
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<h3>d)</h3>
3x = -2y +8
We have a constant with the y-term. To get rid of it, we add its opposite to both sides.
3x -8 = -2y +8 -8
3x -8 = -2y
As before, we divide by the coefficient of y:
(3x -8)/(-2) = (-2y)/(-2)
-3/2x +4 = y
y = -3/2x +4
