Question 63716: can you please helm me on these equations.thank you
1. Find the slope of the line that passes through the points (-3, -5) and (3, 2).
2. Find the equation, in slope-intercept form, of the line that passes through the points (-3, 1) and (-2, -5).
3. Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x – 2y = 24 and passing through (1, 3).
4. Solve the system of equations using the substitution method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
7x + y = 1
3x + 2y = -9
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Find the slope of the line that passes through the points
(-3, -5) and (3, 2).
slope = [2--5]/[3--3]=7/6
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2. Find the equation, in slope-intercept form, of the line that passes through the points (-3, 1) and (-2, -5).
slope = 6/-1=-6
Equation of the line:
y=mx+b; you are given x,y,and m to solve for b, as follows:
1=-6(-3)+b
1=18+b
b=-17
EQUATION:
y=-6x-17
3. Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x – 2y = 24 and passing through (1, 3).
If x-2y=24, y=(1/2)x-12
Any line perpendicular to it has slope m=-2
The line with slope -2 and passing through (1,3):
3=-2*1+b
b=5
EQUATION:
y=-2x+5
Standard form is ax+by=c
2x+y=5
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4. Solve the system of equations using the substitution method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
1st: 7x + y = 1
2nd: 3x + 2y = -9
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Solve 1st for y to get: y=-7x+1
Substitute into 2nd to get:
3x+2(-7x+1)=-9
3x-14x+2=-9
-11x=-11
x=1
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Substitute in y=-7x+1 to get
y=-7*1+1=8
Solution:
x=1, y=8
Cheers,
Stan H.
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