Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)
Start with the given equation
Subtract 2x from both sides
Simplify
Divide both sides by -5 to isolate y
Break up the fraction on the right hand side
Reduce and simplify
The original equation (standard form) is equivalent to (slope-intercept form)
The equation is in the form where is the slope and is the y intercept.
So the slope is which means the answer is D) Answer by TP(29) (Show Source): You can put this solution on YOUR website! To do this question you must be aware of the following.
The general equation of a straight line is written as y=mx+c where m is the slope(or gradient)of the line and c is the y coordinate where the line cuts the y axis( c is also called the y intercept).
In the more difficult questions you must also know how to re-arrange equations.
Here is a simple example.
Suppose the equation of a straight line is y=3x+2.
If we compare this to the general equation y=mx+c then we can see that the number next to x(called the coefficient of x) is 3 in our equation and this is in the place taken up by m in the general equation.
So we can say that m=3. But m is the slope of the line so the slope of the line that has equation y=3x+2 is 3.
Also comparing both equations we can see that c=2. This means that the line with equation y=3x+2 cuts(or crosses) the vertical y axis at 2 units up from the origin.
Examples: The line with equation y=5x+7 has a slope of 5 and and cuts the y axis at 7 up.
The line with equation y=-4x-3 has a gradient of -4 and cuts the y axis at -3(3 below the origin).
So to identify the slope and the y coordinate where a line crosses the y axis your equation must be in the form y=mx+c.
If the equation you are given is not in this form then you have to re-arrange it so that it is in the form y=mx+c.
Example: Find the slope of the straight line that has the equation 4y-9x=12
So 4y-9x=12 has to be re-arranged into the form y=mx+c before we can say what its slope is.
Solution: Given 4y-9x=12
Add 9x to both sides
This gives 4y=12+9x or 4y=9x+12.
But we need to have just y(or 1y) by itself on the left-hand side of the equal sign.
To get this we must now share(divide)both sides of the equation 4y=9x+12 by 4.
When we do this we get that 4y/4=9x/4+12/4.
This simplifies to: y=2.25x+3 (since 9/4=2.25)
So now we have the equation in the form y=mx+c and we can see that the number next to the x is 2.25 so the slope of the line is 2.25ANS.
Now for your equation 2x-5y=3.
If we add 5y to both sides of the equation we get: 2x-5y+5y=3+5y
This simplifies to 2x=3+5y or 2x=5y+3
Now swap sides to get: 5y+3=2x
We now need to get rid of the +3 on the left-hand side so that we are just left with 5y on the left-hand side.
To do this we must subtract 3 from both sides so that we get:5y+3-3=2x-3.
This simplifies to 5y=2x-3.
(We're neally there, just one more step!)
We need to have just y or 1y(same thing) on the left-hand side and so that 5 next to the y has to be changed to a 1.
We do this by sharing(dividing)both sides by 5 so that we get: 5y/5=2x/5-3/5.
This simplifies to y=0.4x-0.6 (since 5/5=1, 2/5=0.4 and 3/5=0.6).
So we (finally) have y=0.4x-0.6.
This means that the slope of your line is 0.4 and it cuts the y axis at 0.6 below the origin (below because its -0.6 in the equation and not +0.6).
So looking at the list of answers that you have to choose from for the slope the correct answer is d)2/5 (since 0.4=2/5).