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Math Help - Graphing Linear equations?

  1. #1
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    Graphing Linear equations?

    Here are some examples that my teacher wanted us to try over the weekend.
    FOr each of these linear equations, sketch a graph, and I just want to know how I go about doing that or solving these? Thanks

    a.) y=3/2x+4
    b.) 4x+2y-7=0
    c.)2(x+y)=3x+y
    d.)3(x+y)=x+3y+6


    2.) Consider the line whoes equation in (x,y) is 5x+3y=4

    WHat is the lines slope?
    Find an equation for the parallel line through 3,2
    Find an eqation for the perpendicular line through 3,2
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  2. #2
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    Hi,

    a.) y=3/2x+4
    b.) 4x+2y-7=0
    c.)2(x+y)=3x+y
    d.)3(x+y)=x+3y+6
    In order to graph these you need to first solve for y. Then you will know where the graph crosses the x and y axis and what the slope is. The slope is the coefficient in front of the x term. For example, for y=3/2x+4 the slope is 3/2 and it crosses the y axis at 4. Therefore, you would mark (0,4) and go up 3 spaces and over 2 and up 3 more spaces and over 2 and keep doing this until you see where the line goes.
    2
    .) Consider the line whoes equation in (x,y) is 5x+3y=4

    WHat is the lines slope?
    Find an equation for the parallel line through 3,2
    Find an eqation for the perpendicular line through 3,2
    What is the lines slope?
    The slope of the line is the coefficient of the x term. For example, in part a. the coefficient is 3/2. Therefore, the slope of the line is 3/2. For this one you have to first solve for y. Do you know how to do that?

    Find an equation for the parallel line through 3,2
    When two lines are parallel to each other, that means that the slopes are the same. Therefore, in order to solve this, you need to use the equation y=mx+b. Do you know how to use this equation?
    You then need to plug in the (3,2) and the slope you found in part a.

    Find an equation for the perpendicular line through 3,2
    When a line is perpendicular to another line, that means that the slope is the negative inverse. You need to do the same exact thing that you did to answer the second question, only this time the slope is the negative reciprical.

    I hope this helps
    Regards
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  3. #3
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    for B on the first part, I got y=7/2-4x as answer? Is that right?
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  4. #4
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    Ok figured b out to be y=-2x+7/2 and then just put figures in for x to figure out the cordinates. Can someone help me with c and d?
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  5. #5
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    Can someone help me with D? Thanks
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by MathMack View Post
    d.)3(x+y)=x+3y+6
    3(x + y) = x + 3y + 6 ............expand

    \Rightarrow 3x + 3y = x + 3y + 6 ...........gather all x's on one side and all y's on the other

    \Rightarrow 2x = 6

    \Rightarrow x = 3

    this is a vertical line along which the x-coordinate is always 3
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    in general, to plot a line, you need only two points. the x- and y-intercepts are usually the most ideal points to find. the y-intercept is explicit in the equation of a line, it is the b in y = mx + b. for the x-intercept, set y = 0 and solve for x. thus you will have two points: (0,b) and (a,0) where b is the y-intercept and a is the x-intercept. plot these points on your axis and draw a line through them
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