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How do you change an equation of point-slope intercept to standard form?
Wiki User
∙ 15y ago
The pint-slope intercept form of the equation of a line is: y = mx + b
The general form is: Ax + By = C. So,
y = mx + b subtract mx to both sides;
y - mx = b
-mx + y = b multiply by -1 to both sides;
mx - y = -b This is the general form.
Wiki User
∙ 15y ago
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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.
What is the equation of a line in standard form?
The standard form equation of a line is y=mx+b. M represents the slope; slope is the change in x over the change in y. B represents the y-intercept.
Can a linear equation be graphed with only the slope and intercept when it is in standard form?
That's all you need to know in order to draw the graph. Note that it doesn't matter what form the equation is written in. The form of presentation doesn't change the slope or intercept.
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 is the part of the slope intercept form that represents the rate of change?
y=mx +b is the equation for slope intercept form. y = the output of the equation m = the slope x = the input into the formula b = the y-intercept The slope represents the rate of change. This is because for every input, or x, you put into the equation, is changed by m. So the M portion of this equation would be the rate of change.
How do you change from standard form to slope intercept?
Solve the standard form for the dependent variable, commonly 'y'.
What is the standard form for a slope intercept?
y=mx+b. Standard form is Ax+By=C. To get to standard form from slope intercept, Move slope times x over to the y side and change the positive or negative sign.
Who do you change from slope intercept form to standard form?
This is stupid! Why do you even need m help?!
What is the parallel equation to y equals 2x plus 5?
y = 2x+10 Just change the y intercept.
Find the x intercept or intercepts and the coordinates of the vertex for the parabola x2-4x-12 if there is more than one x intercept separate them with commas?
The x-intercept of an equation is any location where on the equation where x=0. In the case of a parabolic function, the easiest way to obtain the x intercept is to change the equation into binomial form (x+a)(x-b) form. Then by setting each of those binomials equal to zero, you can determine the x-intercepts.
Can you write an equation in standard form for a line satisfying the given conditions through the point 0 and 4 with a slope of -4.5?
You use slope intercept (y=mx+b) to find yourb(y-intercept) 4=-4.5(0) + b 4=b therfore y=-4.5x + 4. Then you change it into standard form (Ax + By = C) y= -4.5x +4 4.5x + y =4 is your answer.
How do you write 8x plus 4y equals 5 in slope intercept form?
You have to solve the equation for "y", in other words, change it to a form where "y" is on the left, and everything else to the right. You will get an equation of type y = ax + b, where a is the slope, and b the y-intercept.
How do you find slope intercept form out of a equation equal to x?
The simplest way is to change the subject of the formula so that it is in the form y = mx + c. There are alternatives, but a lot more work. Differentiate the equation equal to x, and solve for dy/dx (that is the slope). Substitute x = 0 in the original equation and solve for y (that is the intercept).
