You can put this solution on YOUR website! -7x+4y=12 is the problem i am needing help with
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It's not a problem, it's an equation.
Step 1, what do you want to do?
You can put this solution on YOUR website! Given;
(1) -7x + 4y = 12
This is the standard form of the linear equation that relates the two variables x and y, given by
(2) Ax + By = C where you can compare coefficients of x, y and a constant to get
(3) A = -7, B = 4 and C = 12. The standard form is used in most computer programs to solve system of equations.
Another form of the linear equation is the intercept form given by
(4) x/(xint) + y/(yint) = 1
To put your equation of (1) into this form divide both sides by 12 to get
(5) -7/12x + 4/12y = 12/12 or
(6) x/(-12/7) - y/(12/4) = 1
Now compare the coefficients of (4) and (6) to get
(7) x-int = -12/7 and
(8) y-int = 3
If you draw a line through the points (-12/7,0) and (0,3) on a x-y graph you get the line of the linear equation given by (1).
The third form of the linear equation is the slope-intercept form given by
(9) y = mx + b
where m is the slope of the line y vs x and b is the y-intercept (value of y when x = 0)
You must perform two arithmetic steps with (1) to put it in the form of (9). The first step is to subtract the x-term from both sides to get
(10) -7x -(-7x)+ 4y = 12 - (-7x) or
(11) 4y = 12 + 7x
The second step is to divide both sides of (11) by the coefficient of y and get
(12) 4y/4 = 12/4 + 7x/4 or
(13) y = (7/4)x + 3
The constants m and b can be obtained by comparing the coefficients of (9) and (13) to get
(14) m = 7/4 and b = 3
The line you draw above wil have a slope equal to m = 7/4 and a y-int equal to b = 3
If you draw a line through the point (0,3) with a slope of 7/4 (go right 4 units then up 7 units to get a second point) you will the same graph as above.
This third form is useful in algbra when dealing with one or two linear equations.
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