Answer:
1a. y = 5x +3
1b. y = -1/7x + 2
1c. y = 2x +3
2a. y = -1/2x +3; slope = -1/2, y-intercept = +3
2b. y = 3/2x +6; slope = 3/2, y-intercept = +6
Explanation:
Apparently the "y-intercept form" referred to is the one more commonly called "slope-intercept form." That form is ...
y = mx + b . . . . . . . . m is the slope; b is the y-intercept
You arrive at this form by solving each equation for y. You do that the same way you solve any equation for any variable: undo what is done to the variable of interest.
In these general form equations, the y-variable term has a value multiplying y and some other terms added to that. First of all, you subtract the added terms (from both sides of the equation). This transforms ...
ax +by +c = 0
into
by = -ax -c
Next, you divide by the constant that is multiplying y. Of course all terms on both sides of the equation are divided by that, so you now have ...
y = (-a/b)x -c/b
The slope is -a/b, and the y-intercept is -c/b.
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1a. 5x -y +3 = 0
-y = -5x -3 . . . . . subtract non-y terms
y = 5x +3 . . . . . . divide by -1
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1b. x +7y -14 = 0
7y = -x +14 . . . . . subtract non-y terms
y = -1/7x +2 . . . . .divide by 2
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1c. 6x -3y +9 = 0
-3y = -6x -9 . . . . subtract terms not containing y
y = 2x +3 . . . . . . divide by -3
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2a. x +2y -6 = 0
2y = -x +6 . . . . . subtract non-y terms
y = -1/2x +3 . . . . divide by 2 -- this is graphed as the red line below
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2b. 3x -2y +12 = 0
-2y = -3x -12 . . . . subtract non-y terms
y = 3/2x +6 . . . . . divide by -2 -- this is graphed as the blue line below
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Comment on the 2nd problem
Of course, the y-intercept (constant term in slope-intercept form) is the point on the y-axis where the line crosses. The slope tells you the ratio of "rise" to "run". That is, a slope of -1/2 means the line drops one unit for each 2 units it goes to the right. A slope of 3/2 means the line increases (rises) by 3 units for each 2 units it goes to the right.