Answer:
4) 3, -2, -8
5) -7
6) E
7) D
8) 5, -1, 34
Explanation:
4) There are at least two prominent points on line EF: (0, -4) and (6, 5). From there, we can find the slope-intercept formula of it.
The slope: (5 + 4) / (6 - 0) = 9 / 6 = 3 / 2
The intercept: (0, -4)
So, we have y = 3/2x - 4.
-3/2x + y + 4 = 0
Multiply every term by 2.
-3x + 2y + 8 = 0.
But the question asks for A to be >0! Multiply everything by -1.
3x - 2y - 8 = 0
So, the values of A, B, and C, respectively, are 3, -2, -8.
5) There are at least two prominent points on line GH: (-9, 4) and (-1, 2). From there, we have...
The slope: (4 - 2) / (-9 + 1) = 2 / -8 = -1/4
y = -1/4x + b
2 = (-1/4 * -1) + b
2 = (1/4) + b
b = 1.75; or 1 and 3/4; or 7/4.
Then, we have our intercept: 7/4.
We have an equation in slope-intercept form: y = -1/4x + 7/4
1/4x + y - 7/4 = 0
Multiply everything by 4.
x + 4y - 7 = 0.
The value of C is -7.
6) Lines that are parallel to the y-axis are vertical lines, which means that the x-values never change. We are looking for an equation where x = 3. That is code letter E.
7) Lines perpendicular to the y-axis are horizontal lines, which means that the y-values never change. We are looking for an equation where y = -5. That is code letter D (y + 5 = 0; y = -5).
8) A line parallel to 5x - 8y + 12 = 0 would have the same slope as it.
5x - 8y + 12 = 0
-8y = -5x - 12
y = 5/8x + 3/2
So, the line should have a slope of 5/8.
3 = (5/8) * (-2) + b
3 = -10/8 + b
3 = -5/4 + b
b = 3 + 5/4
b = 4 and 1/4; 17/4.
y = 5/8x + 17/4
-5/8x + y - 17/4 = 0
Multiply all terms by 8.
-5x + y - 34 = 0
Multiply all terms by -1.
5x - y + 34 = 0.
The values of A, B, and C, respectively, are 5, -1, 34.
I REALLY hope this helps because my brain kinda hurts now XD Have a great day!