math help!!?

Question

Write the equation of the lines passing through each of the given points. Write your results in slope-intercept form, where possible.
(-1, 3) and (4,-2)

24. (2,-3) and (2, 4)

36. Write the equation of the line L satisfying the given geometric conditions.
L has y-intercept (0,-3) and is parallel to the line with equation

40. L has y-intercept (0, 2) and is perpendicular to the line with equation 2x-3y=6

thats
Write the equation of the lines passing through each of the given points. Write your results in slope-intercept form, where possible.
(-1, 3) and (4,-2)
36. Write the equation of the line L satisfying the given geometric conditions.
L has y-intercept (0,-3) and is parallel to the line with equation y=-2/3x+1

Answer 1

"Slope-intercept form" is y=mx+b

Since slope (m) = rise/run, and
since standard 2-d Cartesian coordinate form is (x,y),

m = (3 - -2)/(-1 - 4); which simplifies to (3+2)/(-5), or 5/-5, or -1

y=-1x+b, and b is where the line crosses the y axis.

For some people, it's easier to remember that x is ALWAYS zero when you're solving for b, than it is to think of "where on the y axis will the line cross."

I find it easy to go from left-to-right, so:

we know that at y= 3, x= -1; therefore the absolute value of the distance along the x axis to the y axis is 1 (the absolute value of -1 is 1).

we also know that m= -1;
therefore (3 +(-1 * 1)) = 3-1 = 2

So, y= -1x + 2, which can be further simplified to y= -x+2

Depending on your instructor, one answer may be considered correct and the other considered incorrect, but they're mathematically the same. Technically, the former (y= -1x + 2) is the more literally correct, given the parameters you indicated.

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Repeat the foregoing process for 24.
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For 36:

b is given by the coordinates (0,-3), so b= -3

Since the line has to be parallel to another line, it has to have the same slope as the other line. Remembering the slope-intercept form is y=mx+b, if the equation for one line is y=-2/3x+1, then you know that m= -2/3.

y= -2/3x-3
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For 40:

b is 2 (see above for explanation how to know this)

Change 2x-3y=6 into slope-intercept form: y= -2/3x+2

The slope perpendicular to -2/3 is 3/2 (swap numerator & denominator, change the sign) -- so:

y=3/2x+2 or y=1.5x+2

As a bonus for your own info, the line "L" crosses the line perpendicular to it in the problem (2x-3y=6) at the y-intercept.

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Answer 2

i only no how to find the eqution. ok it is 2