SOLUTION: Find the equation of line point-sloope and slope-intercept form that meet the following conditions. 1. The line passes through the points (-3,-1) and (3,5) 2. The line passes

Algebra ->  Linear-equations -> SOLUTION: Find the equation of line point-sloope and slope-intercept form that meet the following conditions. 1. The line passes through the points (-3,-1) and (3,5) 2. The line passes      Log On


   

Question 665989: Find the equation of line point-sloope and slope-intercept form that meet the following conditions.
1. The line passes through the points (-3,-1) and (3,5)
2. The line passes through the point (3,7) and is parellel to the line x + 4y = 12.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1.The line passes through the points (-3,-1) and (3,5)

Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (-3, -1) and (x2, y2) = (3, 5).
Slope a is a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%285--1%29%2F%283--3%29+=+1.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or 1%2A-3+%2Bb+=+2. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=-1-1%2A-3+=+2.

y=(1)x + (2)

Your graph:





2. The line passes through the point (3,7) and is parellel to the line x+%2B+4y+=+12.

x+%2B+4y+=+12....write in slope-intercept form
4y+=-x%2B+12
4y+=-%281%2F4%29x%2B+3

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is -1%2F4 (its from the slope of y=%28-1%2F4%29%2Ax%2B3 which is also -1%2F4). Also since the unknown line goes through (3,7), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-7=%28-1%2F4%29%2A%28x-3%29 Plug in m=-1%2F4, x%5B1%5D=3, and y%5B1%5D=7



y-7=%28-1%2F4%29%2Ax%2B%281%2F4%29%283%29 Distribute -1%2F4



y-7=%28-1%2F4%29%2Ax%2B3%2F4 Multiply



y=%28-1%2F4%29%2Ax%2B3%2F4%2B7Add 7 to both sides to isolate y

y=%28-1%2F4%29%2Ax%2B3%2F4%2B28%2F4 Make into equivalent fractions with equal denominators



y=%28-1%2F4%29%2Ax%2B31%2F4 Combine the fractions



y=%28-1%2F4%29%2Ax%2B31%2F4 Reduce any fractions

So the equation of the line that is parallel to y=%28-1%2F4%29%2Ax%2B3 and goes through (3,7) is y=%28-1%2F4%29%2Ax%2B31%2F4


So here are the graphs of the equations y=%28-1%2F4%29%2Ax%2B3 and y=%28-1%2F4%29%2Ax%2B31%2F4



graph of the given equation y=%28-1%2F4%29%2Ax%2B3 (red) and graph of the line y=%28-1%2F4%29%2Ax%2B31%2F4(green) that is parallel to the given graph and goes through (3,7)