SOLUTION: Hello Friends, Help! So lost on these Slope and Linear scenarios. 1. Given the linear equation y=-3/4x-3, find the y-coordinates of the points (-8, ), (-4, ), and (4, ).

Algebra ->  Linear-equations -> SOLUTION: Hello Friends, Help! So lost on these Slope and Linear scenarios. 1. Given the linear equation y=-3/4x-3, find the y-coordinates of the points (-8, ), (-4, ), and (4, ).      Log On


   

Question 1001080: Hello Friends,
Help! So lost on these Slope and Linear scenarios.
1. Given the linear equation y=-3/4x-3, find the y-coordinates of the points
(-8, ), (-4, ), and (4, ).Plot those points and graph the linear equation.
2. Given the linear equation y=-1/3x+6, find the y-coordinates of the points
(-9, ), (-3, ), and (6, ). Plot those points and graph the linear equation.

3. Write the slope-intercept equation for the line that passes through (14, -2) and is perpendicular to 7x – 10y = 18
4. Write the slope-intercept equation for the line that passes through (1, -9) and (3, -1).
Thanking you in advance
Betty
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1. Given the linear equation y=-%283%2F4%29x-3, find the y-coordinates of the points
(-8, 3 ), =>y=-%283%2Fcross%284%291%29%28-cross%288%292%29-3=>y=-%283%29%28-2%29-3=>y=6-3=>y=3
(-4,0 ), =>y=-%283%2Fcross%284%291%29%28-cross%284%291%29-3=>y=-%283%29%28-1%29-3=>y=3-3=>y=0
(4,-6 )=>y=-%283%2Fcross%284%291%29%28cross%284%291%29-3=>y=-%283%29%281%29-3=>y=-3-3=>y=-6

Plot those points and graph the linear equation.




2. Given the linear equation y=-%281%2F3%29x%2B6, find the y-coordinates of the points
(-9,9 ), =>y=-%281%2Fcross%283%291%29%28-cross%289%293%29%2B6=>y=-%281%29%28-3%29%2B6=>y=3%2B6=>y=9
(-3,7 ),=>y=-%281%2Fcross%283%291%29%28-cross%283%291%29%2B6=>y=-%281%29%28-1%29%2B6=>y=1%2B6=>y=7
(6,4 )=>y=-%281%2Fcross%283%291%29%28cross%286%292%29%2B6=>y=-%281%29%282%29%2B6=>y=-2%2B6=>y=4
Plot those points and graph the linear equation.



3. Write the slope-intercept equation for the line that passes through (14,+-2) and is perpendicular to 7x+-10y+=+18
the slope-intercept form of the given equation
7x+-18+=+10y
y=+%287%2F10%29x+-9%2F5+

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


Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of 7%2F10, you can find the perpendicular slope by this formula:

m%5Bp%5D=-1%2Fm where m%5Bp%5D is the perpendicular slope


m%5Bp%5D=-1%2F%287%2F10%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%2810%2F7%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-10%2F7 Multiply the fractions.


So the perpendicular slope is -10%2F7



So now we know the slope of the unknown line is -10%2F7 (its the negative reciprocal of 7%2F10 from the line y=%287%2F10%29%2Ax-9%2F5). Also since the unknown line goes through (14,-2), 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%2B2=%28-10%2F7%29%2A%28x-14%29 Plug in m=-10%2F7, x%5B1%5D=14, and y%5B1%5D=-2



y%2B2=%28-10%2F7%29%2Ax%2B%2810%2F7%29%2814%29 Distribute -10%2F7



y%2B2=%28-10%2F7%29%2Ax%2B140%2F7 Multiply



y=%28-10%2F7%29%2Ax%2B140%2F7-2Subtract -2 from both sides to isolate y

y=%28-10%2F7%29%2Ax%2B140%2F7-14%2F7 Make into equivalent fractions with equal denominators



y=%28-10%2F7%29%2Ax%2B126%2F7 Combine the fractions



y=%28-10%2F7%29%2Ax%2B18 Reduce any fractions

So the equation of the line that is perpendicular to y=%287%2F10%29%2Ax-9%2F5 and goes through (14,-2) is y=%28-10%2F7%29%2Ax%2B18


So here are the graphs of the equations y=%287%2F10%29%2Ax-9%2F5 and y=%28-10%2F7%29%2Ax%2B18




graph of the given equation y=%287%2F10%29%2Ax-9%2F5 (red) and graph of the line y=%28-10%2F7%29%2Ax%2B18(green) that is perpendicular to the given graph and goes through (14,-2)







4. Write the slope-intercept equation for the line that passes through (1, -9) and (3, -1).

Solved by pluggable solver: Find the equation of line going through 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) = (1, -9) and (x2, y2) = (3, -1).
Slope a is a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%28-1--9%29%2F%283-1%29+=+4.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or 4%2A1+%2Bb+=+-13. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=-9-4%2A1+=+-13.

y=(4)x + (-13)

Your graph:



your equation is:
y=4x+-13