q2
If you mean -x+y = 12 then y = x+12 and so the parallel line will have the same slope but with a different y intercept.
4x+y = 14 will be parallel to the above equation because the slope or gradient remains the same but the y intercept changes.
y = -7x + 6 is the equation of a straight line. It has a slope of '-7' and a y-intercept of '6'. For it to be parallel it must be compared to another line. e.g. y = -7x + 12 is a paralle line However, y = 7x + 6 is NOT a parallel line, because the slope is in a different direction.
Rearranging the original equation, we get y=-(2/3)x+12. Since 12 is the constant, this is the point that the line of this equation will cut the y-axis if x=0. Therefore, -(2/3) is the gradient and for an equation to produce a parallel line, the gradient must be equal. Summing up, y=-(2/3)+c (where c equals any real number) would be parallel
q2
If you mean -x+y = 12 then y = x+12 and so the parallel line will have the same slope but with a different y intercept.
14
4x+y = 14 will be parallel to the above equation because the slope or gradient remains the same but the y intercept changes.
Lines parallel to the line would have the same slope, which is 3/4. (0.75) 3x-4y = 12 3x-12 = 4y y = 3/4 x - 3 The y-intercept is -3 and the slope is 3/4.
Any equation of the form 2x + 3y = c, where c is a constant value, represents a line parallel to the given line 2x + 3y = 12.
y = -7x + 6 is the equation of a straight line. It has a slope of '-7' and a y-intercept of '6'. For it to be parallel it must be compared to another line. e.g. y = -7x + 12 is a paralle line However, y = 7x + 6 is NOT a parallel line, because the slope is in a different direction.
Rearranging the original equation, we get y=-(2/3)x+12. Since 12 is the constant, this is the point that the line of this equation will cut the y-axis if x=0. Therefore, -(2/3) is the gradient and for an equation to produce a parallel line, the gradient must be equal. Summing up, y=-(2/3)+c (where c equals any real number) would be parallel
The second equation works out as y = -1/2x+6 therefore it is perpendicular
They don't. The line is parallel. ( 4x-8x=12 simplifies to y-2x+3, which has the same slope as y=2x+2)
-1
y = (a + 12)(x + 3) (line 1)y = 4ax (line 2)Since the equation of the second line is in a slope-intercept form, write the equation of the first line in the slope-intercept form, y = mx + b, where m is the slope of the line.y = (a + 12)(x + 3)y = a(x + 3) + 12(x + 3)y = ax + 3a + 12x + 36y = ax + 12x + 3a + 36y = (a + 12)x + 3a + 36, where the slope is a + 12y = 4ax, where slope is 4aSince the lines are parallel they must have the same slope. So that,a + 12 = 4a3a = 12a = 4Thus, when a = 4, the parallel lines have a slope of 16.