When graphing an equation of the form y=mx+c, how do you know which variables represent m, x and c?
To know m,x & c, first express the equation in the form of a linear eqution.Example - Let's say we have a linear equation: 2x + y = 4Convert it in the form: y = mx + cThe equation will become: y = -2x + 4 So, m = -2 (Slope/gradient of the line)and, c = 4 (Y intercept)As, s = ut + 1/2(at^2) is a quadratic equation, hence it cannot be expressed in the form of y = mx + c.But, it can be expressed in the form of the graph of a quadratic equation of the form y = ax^2 + bx + c.Where, a, b, c are constants.This graph can be represented by a parabola. Let's try to express the motion of equation into that form.s = (1/2a)t^2 + ut + 0here, a = 1/2a (Assuming acceleration is constant) b = u (initial speed is constant) c = 0 (Constant) y = s x = tNow, the parabola of a quadratic equation depends upon the nature of the constant 'a' and discriminant 'D'(which is b^2 - 4ac).Assume, a>0 (Positive acceleration)And, with c = 0, D will be b^2 > 0So, the graph will be a parabola opening upwards and would look like the one below.where,Y axis - SpeedX axis - TimeShaded region - DistanceTop-most curve - Equation of motion Hope this helps. Feel free to correct me if something is wrong.
How do I make these equations in function form?
Well if I'm looking at these equations right... 1. 7x - y = 0: You need to put "y" by itself, and when you do that, the sign changes. So what you would have as the answer would be... y = 7x. Because when you put "7x" on the other side, the sign changes, and you can't have "y" and negative, so you would divide both sides by "-1" and there you have it. A: Y = 7x 2. 15x + y = 20 A: y = -15x + 20 3. y + 6x - 12 = 0 A: y= -6x +12 4. 6y - 3x = 12: Now here, doing the same process, you would have "6y = 3x + 12" divide both sides by 6, so that you get "y" by itself. A: y = 1/2x + 2 5. 3x - 2y = 6 -2y = -3x + 6 A: y = 3/2x - 3 6. 4x - 12y + 24 = 0 -12y = -4x + 24 A: y = 1/3x - 2
Write this equation in standard form y=4x+x?
First you have to understand what standard form is. For a linear equation standard form is Ax + By = C A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers. Now putting the equation into that form y=4x+x Add like terms y = 5x Subtract y from both sides 0 = 5x - y Flip the equation 5x - y = 0 <------ m11112013
Put 7x-y=0 in function form?
You are right but you must wright y = ax + b : y = 7x
What is the double intercept form of a linear equation?
In the double-intercept form of a line the x-intercept is a and the y-intercept is bThe given line (x/4) - (y/9) = 1 can be written as (x/4) + (y/-9) = 1so the x-intercept is (4, 0) and the y-intercept is (0, -9)the slope = (-9 - 0) /(0 - 4) = -9 / (-4) = 9/4BUT the way the question is worded I think they want you to find the x and y-intercepts then note that they are the a and b in the equation so I'll do that by writing the given equation in slope-intercept form y = mx + b where m is the slope and b is the y-intercept:a) (x/4) - (y/9) = 1Multiplying both sides by 4 x 9 = 36:9x - 4y = 364y = 9x - 36y = (9/4)x - 9so slope = 9/4y-intercept is (0, -9) ←←[the corresponding x-coordinate for the y-intercept is ALWAYS zero]the x-intercept is when y = 0so subsing:0 = (9/4)x - 9(9/4)x = 9x = 4so the x-intercept is (4, 0) ←←[the corresponding y-coordinate for the x-intercept is ALWAYS zero]b) comparing the results from part (a) with the given equation written in the double-intercept form (x/4) + (y/-9) = 1a is the x-coordinate of the x-intercept of the lineand b is the y-coordinate of the y-intercept of the linec) 5x + 2y = 30To get the y-intercept set x = 0 and solve for y:so when x = 0, 0 + 2y = 302y = 30y = 15 → so for the double-intercept form of the line b = 15to get the x-intercept set y = 0 and solve for x:5x + 0 = 305x = 30x = 6 → so for the double-intercept form of the line a = 6so the required equation written in double-intercept form is:(x/6) + (y/15) = 1
Find an equation for the line parallel to 3x+5y-4=0, with the same x-intercept as 2x-3y-6=0. Include steps?
To solve the problem you need to understand that parallel lines have the same slope, so you want to find the slope of the line in the first equation, and the x-intercept of the second. First put 3x + 5y - 4 = 0 into slope intercept form which is y = mx +b where m = slope and b = y-intercept. 5y = -3x + 4 y = -3/5x + 4/5 Do likewise for 2x -3y - 6 = 0 3y = 2x - 6 y = 2/3x - 2 To find the x-intercept set y = 0 and solve for x. Here y = 0 when x = 3 So now we have a slope (-3/5) and a point on the line (3,0) - the x-intercept. We can now plug these values into the point-slope formula which is: y - y1 = m(x - x1) where m = slope and (x1,y1) is a point on the line. y - 0 = -3/5(x - 3) y = -3/5x + 9/5 In standard form: 3/5x + y - 9/5 = 0 or 3x + 5y - 9 = 0
I have to graph this equation 2x+3y<30 ... how do i solve it to graph it?
First graph the line 2x + 3y = 30 by putting it into slope intercept form y = -(2/3)x+10 and drawing a line with slope -2/3 and y-intercept 10. Then the graph of 2x + 3y < 30 should either be all the points to the left of the line you just drew or all the points tot he right of the line you just drew. To figure out which, pick a point, say (0,0), and plug it into the inequality. Plugging in (0,0) we get 0<30, which is true, so the point (0,0) should be included in the graph. So shade in whichever side of the line contains the point (0,0). Also, since the inequality is strictly less than and not less than or equal, the line itself should not be included in the graph. Thus the line should be dotted, and not solid.
How Do I find the slope, x-int, and y-int of this equation?
First we define what the intercepts are. Basically you set the other variable to zero if you want to solve for x or y. We'll do that first. X int: y=0 ==> 15x = 27; x = 9/5 Y int: x=0 ==> -9y = 27; y = -3 Slope: We have to put the equation into y=mx+b form first. The m is your slope. 15x-9y=27 -9y=27-15x 9y=15x-27 y=x(5/3) - 3 Therefore, your slope is 5/3.
Where does the line represented by the equation -2x + y-7=0 intersect the y axis?
U can fine this by 2 methods atleastIf u want to find the intercept on y axis than at y axis x cordinate will be 0 so simply put x=0 so u will get 7Now the other method is to create this equation of line in intercept form that is . (x/a)+(y/b)=1. ———————(A)Wher a and b are intercept on x and y axis respectivelyNow to create this we can write our equation as-2x +y= 7. —————-(B)Now as eqa. A has 1 at right soDivide equa B by 7(-2x/7)+(y/7)=1Now as equation A has coefficients of y and x as 1 so[x/(-7/2)]+(y/7)=1. ——————-(C)So on comparing euation C by AWe geta=(-7/2)b=7So line intersects x axis at (-7/2) and y ant 7…