Question

In need of some help with 5 problems.. Help ?
1. Is the point (2,-3) on the line x+2y=-3? Explain your answer.
2. Identify which lines are parallel. Explain your answer.
y=2x+5 -4x+2y=6 -12x+3y=15 .
3. Write an equation in slope- intercept form of the line that passes through the points (2,4) and (5,10) .
4. Write an equation slope - intercept form of the line that is parallel to y=2x+3 that passes through the point (2,5) .

Answer 1

regarding the attached pic, the first 2 are perpendicular because their slopes' product = -1
i.e. m1 * m2 = -(1/2) * 2 = -1

you know that the equation for a line is
y = mx + b, where m is the slope, b is the y-intercept

Answer 2

regarding #1 in the main question, substitute x = 2 and y = -3 in the given equation and see if you get -3, this should be quiet easy, right?

Answer 3

#2 parallel lines have equal m's (slopes)
convert -4x+2y=6 to the following
2y = 4x + 6 .... divide both sides by 2 and u get
y = 2x + 3 .... now this looks similar to which from above ? the first or the third (the third will need to be simplified down to y = 4x + 5).... which two equations have the same slope or m ?

Answer 4

the formula for the slope is ?
m = (y2 - y1) / (x2 - x1)
= ... can u find it knowing that
y2 = 10
y1 = 4
x2 = 5
x1 = 2


then the line equation becomes
y = mx + b

where b is the y-intercept, can u find it?

Answer 5

Thank-You ! I think I know how to do them now. For the last 1 was it y=3x+6 ? Where b is the y-intercept, Is it 6 ?

Answer 6

yes 6 is the y-intercept

Answer 7

Thanks!