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How do you graph 3x plus 4y equals -4?
3x+4y=-4 can be graphed on a graphing calculator or by changing the form of the equation from standard form to slope intercept form. Rearrange the equation 4y=-3x-4 divide by 4 y=(-3/4)x-1 Now, you can simply graph the equation using the y intercept and the slope of the equation. A good point to start with is (0,-1) you know this point is the y intercept because of the standard y intercept equation y= mx+b where b is the y intercept and m is the slope. From the y intercept of (0,-1) you can then graph using the slope which is the change of y over change in x. So you would move up 3 and to the left 4 since the slope is negative. You can also move down three and to the right 4. Then continue, this process until you have the equation graphed. It should be a straight line.
What are the intercepts for the equation 18x-9y plus 3z equals 18?
18x - 9y + 3z = 18First, just to clean it up a bit, divide both sides of the equation by 3.(This doesn't change the equation or its graph in any way.)6x - 3y + z = 6At the 'x'-intercept, 'y' and 'z' are zero:6x = 6x = 1At the 'y'-intercept, 'x' and 'z' are zero:-3y = 6-y = 2y = -2At the 'z'-intercept, 'x' and 'y' are zero:z = 6
What is the definition of linear equation?
A linear equation has a constant rate of change, or slope (change in y (dependent) value over change in x (independent) value), when graphed forms a straight trend line, and is in the format y=mx+b (y is dependent value, m is slope, x is independent value, and b is the y-intercept (the value of y when x=0).
How do you graph using the rate of change and initial value?
Normally on the Cartesian plane using as for example the straight line equation y = mx+c whereas m is the gradient or slope and c is the y intercept.
How do you solve the equation of each line in standard form if i am only given the x-intercept and the y-intercept?
Answer: Given y-intercept b and x-intercept x2 , the equation of the line in standard form will be: bx+x2y-bx2 =0Explanation oneFirst off, the standard form of an equation is Ax +By = C.If you have both intercepts, then you have two points. A line can easily be defined by two points. If we let the y intercept be y1 i.e the point P1 =(0,y1) and the x intercept be x2 i.e. the point P2 =(x2,0). Then we can use those two points to calculate slope:m= (y1-0)/(0-x2)= -(y1/x2).Now, we can use the point slope formula.That formula is (y-y1)=m(x-x1 ) where (x1 ,y1 ) is any given point. ( NOT a variable, but a specific point)Now since we have two points P1 and P2 we can use either.Let's use P2(y-0)=m(x-x2) Simplify:y = mx - mx2Now note that (mx2 ) is just a number, not a variable. It is the slope multiplied by the x-intercept. We can call mx2 =CSo lastly, we put the equation in standard from.Ax+By+C=0-mx+y+mx2 =0We are not quite done. Remember we know exactly what m is.So let's substitute m=-(y1/x2) into the equation.-(-(y1/x2))x+y-(y1/x2)x2 =0(y1 /x2 )x+y+(-y1)=0or(y1 /x2 )x+y-y1=0We could also be rid of the x2 in the denominator and make it look much nicer.y1x+x2y-x2y1 =0If you prefer, since the y intercept is often denoted by b, we could let y1 =b and we havebx+x2y-x2 b =0(we could take this one step further, let's call the x intercept tthen given b and t we could write the equation in standard form asbx+ty-tb=0)so A=y1B=x2C=-x2y1For instance. if you had P2 =(1,0) and P1=(0,3), you can plug in the values directly from the formula we just calculated. A=3, B=1 and C=-33x+y-3=0If we put this in slope intercept form, we havey=-3x+3 which tells us right away the slope is -3 and the y intercept is 3.If we calculated slope with P2 =(1,0) and P1=(0,3) we would have m=3/-1=-3and y intercept is 3 since we have the point P1=(0,3)So we could write that equation in slope intercept from right away as y=-3x+3or in standard form as 3x+y-3=0Explanation twoThere is a form of the line know as two point form.Given points P1 =(x1 ,y1 ) and P2 =(x2 ,y2 )The equation of the line though those two points is:(y-y1)/(y2 -y1 )=(x-x1)/(x2 -x1)If we now plug in P1 =(0,y1) and P2 =(x2,0)we have(y-y1)/(0 - y1)=(x-0)/(x2)=(y- y1)/ -y1=x/x2 or -(y-y1)/ y1=x/x2Now let's cross multiply so have y1 x=-(y-y1)x2 or after simplifying.y1 x= -yx2+y1x2y1 x + x2 y - y1x2=0 which agrees with our formula above. If we let b=y1 we haveb x + x2 y- bx2=0Technical note: The y intercept is the y-value of the point where the graph of a function or relation intercepts the y-axis of the coordinate system. So if we have y=mx+b, the y intercept is b, and the point (0,b) is on the line.Explanation 3. using a numerical example.Write the information as two ordered pairs like: (0,5) y intercept and (2,0) x intercept.Then use the method you are most familiar with to write the equation.Using the slope formula: m = change in y/ change in x = 0-5/2 -0 = -5/2 is slope.Replace m and b in the slope intercept form so the answer is:y = -5/2 x + 5. This is the equation of a line with intercepts (0,5) and (2,0).To change into Standard form we multiply by 2 to eliminate the fractions so2y = -5x + 10 and then add the 5x term to both sides giving: 5x + 2y =10.
