Answer:
a) 4x -y = 2; (1/2, 0), (0, -2)
b) 3x +y = 5; (5/3, 0), (0, 5)
c) 5x -y = -3; (-3/5, 0), (0, 3)
d) x -y = 7; (7, 0), (0, -7)
e) 8x +y = -12; (-3/2, 0), (0, -12)
Explanation:
The form you have is ...
y = -Ax +C . . . . . where B = 1
You can simply rearrange the coefficients to get the form you want.
For (a), you can identify -A = 4, so A = -4, and C = -2. In the desired form, the equation is then ...
-4x +y = -2
"Standard form" requires the leading coefficient be positive, so you now need to multiply the entire equation by -1:
4x -y = 2
I suspect either of the above answers will satisfy your grader, but I like the latter form better. So, the answers below have the equation multiplied by -1 when A is negative to start with.
Since the given equation is already in slope-intercept form, the y-intercept is read directly from the equation as C.
The x-intercept is the value C/A, where you do need to pay attention to the signs.
Again, for (a), the y-intercept is already known to be -2; the x-intercept is ...
C/A = -2/-4 = 2/4 = 1/2.
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a) A=-4, C=-2, x-intercept = C/A = -2/-4 = 1/2, y-intercept = C = -2. Equation in standard form is 4x -y = 2
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b) A=3, C=5, x-intercept = C/A = 5/3, y-intercept = C = 5. Equation in standard form is 3x+y=5
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c) A=-5, C=3, x-intercept = C/A = 3/-5 = -5/3, y-intercept = C = 3. Equation in standard form is 5x -y = -3
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d) A=-1, C=-7, x-intercept = C/A = -7/-1 = 7, y-intercept = C = -7. Equation in standard form is x -y = 7
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e) A=8, C=-12, x-intercept = C/A = -12/8 = -3/2, y-intercept = C = -12. Equation in standard form is 8x +y = -12