Question 203011: please i need someone to help me with these three problems:
the directions are: find an equation of the line having the given characteristics. Express ypur answer using either the general for or the slope-intercept form of the equation of a line.
1) Slope undefined; passing through (-3,4)
2) x-intercept= -2; passing through (4, -5)
3) y-intercept= -2; passing through (5,-3)
please help me and explain these answers with detail!! Please and Thank you!
Answer by PRMath(133)   (Show Source):
You can put this solution on YOUR website! Question 1) Slope undefined; passing through (-3,4)
When a slope is undefined, the line is a vertical line.
And... vertical lines occur when x equals a number.
In this case, your line passes through (-3, 4).
The "X" in that ordered pair is -3, so your line is x = -3.
If you have a line that says x = -3, then it will go thru (-3, 4)
And, just for your info, when a slope is 0, the line is horizontal.
Undefined does NOT mean "0", k?
So to reiterate:
Vertical lines have an undefined slope.
Horizontal lines have a slope of 0.
Question 2) x-intercept= -2; passing through (4, -5)
If your x intercept is -2, then the ordered pair that represents the x intercept is: (-2, 0).
Why?
Well, when you want an x intercept, you solve for X by making y = 0.
When you want a y intercept, you solve for Y by making x = 0.
You were given the fact that your x-intercept was -2.
Therefore, they are saying to you that when they made y = 0, the x = -2
This is your ordered pair for x = -2 and y = 0 ----> (-2, 0)
So, your line goes thru the point (-2, 0) AND it goes thru (4, -5). You have enough info here to find the SLOPE of a line. How do you determine slope? The formula for slope is:
 SO let's fill in the values for this equation.
 which is:
 which is:
 <---- This is your SLOPE which is represented by "m"
Do you know the POINT SLOPE form of a line? It is this...
You use this equation when you know the SLOPE and point that the line passes thru. We just figured out the slope and they gave you what the line passed thru, so let's just sort of plug in the right values.............
m=
The line passes thru: (4, -5)
y - -5 = -5/6(x - 4) (plugged in the x and y values as well as the slope)
y + 5 = -5/6x + 20/6) (distributed the -5/6)
y = -5/6x + 20/6 - 5 (subtracted 5 from both sides)
y = -5/6x + 20/6 - 30/6 (found a common denominator to add 20/6 - 5)
y = -5/6x - 10/6 (final answer)
Question: 3) y-intercept= -2; passing through (5,-3)
This is solved similar to the above, so I'll not go in as much detail. So here goes:
The y intercept means they solved for Y by making the X = 0. Therefore, they are saying: When x was equal to 0, the y was -2. Therefore, you have:
(0, -2)
This line passed thru (5, -3) so our slope is:
-3 - -2/5 - 0
-3 + 2/5 - 0
 ====> m =
Now plug in the values in the point slope equation of a line..........
y - -3 = -1/5(x -5)
y + 3 = -1/5x + 5/5
y + 3 = -1/5x + 1
y = -1/5x + 1 - 3
y = -1/5x -2
ORRRRR, it is MUCH easier, when you know the Y intercept and the SLOPE to just plug into the SLOPE INTERCEPT equation of a line. That equation is:
y = mx + b
In this equation, m = SLOPE
b = y intercept.
Sooo, they told you that the y intercept was -2
We determined the slope was -1/5
SO we just fill in the values for "m" and "b"
m = -1/5
b = -2
y = -1/5x - 2.
I hope this helps you. :-)
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