SOLUTION: find an equation of the line having the given characteristics X-intercept = 2; passing through (4,-5) also find an equation of the line having the given characteristics

Algebra ->  Linear-equations -> SOLUTION: find an equation of the line having the given characteristics X-intercept = 2; passing through (4,-5) also find an equation of the line having the given characteristics       Log On


   

Question 305838: find an equation of the line having the given characteristics
X-intercept = 2; passing through (4,-5)
also
find an equation of the line having the given characteristics
perpindicular to the line 3x - y + 4 = 0; passing through (-2,2)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
find an equation of the line having the given characteristics
X-intercept = 2; passing through (4,-5)
Assign the values as follows
x1=2, y1=0, (from the x intercept)
x2=4, y2=-5
:
Find the slope
m = %28-5+-+0%29%2F%284+-+2%29 = %28-5%29%2F2 = -2.5
:
Use the point/slope formula; y - y1 = m(x - x1)
y - (-5) = -2.5(x - 4)
y + 5 = -2.5x + 10
y = -2.5x + 10 - 5
y = -2.5x + 5; is the equation passing thru 4,-5, with x intercept of 2
:
also
find an equation of the line having the given characteristics
perpendicular to the line 3x - y + 4 = 0; passing through (-2,2)
:
Arrange the equation in the slope/intercept form to find the slope
3x - y + 4 = 0;
-y = -3x - 4
Multiply by -1
y = 3x + 4
m1 = 3 is the slope
:
Slope relationship to parallel line: m1*m2 = -1, therefore
3*m2 = -1
m2 = -1%2F3; slope of the parallel line
:
Use the point/slope formula: y - y1 = m(x - x1) where x1=-2, y1=2
y - 2 = -1%2F3(x - (-2))
y - 2 = -1%2F3(x + 2)
y - 2 = -1%2F3x - 2%2F3
y = -1%2F3x - 2%2F3 + 2
y = -1%2F3x - 2%2F3 + 6%2F3
y = -1%2F3x + 4%2F3; is the equation of the parallel line