SOLUTION: Hello! Help Its all about graphing. Graph the linear equation using the slope and y-intercept. 1. y=1/5x+2 2. y=2x-3 3. y= -3/4x

Algebra ->  Inequalities -> SOLUTION: Hello! Help Its all about graphing. Graph the linear equation using the slope and y-intercept. 1. y=1/5x+2 2. y=2x-3 3. y= -3/4x       Log On


   

Question 106069: Hello! Help
Its all about graphing.
Graph the linear equation using the slope and y-intercept.
1. y=1/5x+2
2. y=2x-3
3. y= -3/4x


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1. y=%281%2F5%29x%2B2

Solved by pluggable solver: Graphing Linear Equations
In order to graph y=0.2%2Ax%2B2 we only need to plug in two points to draw the line

So lets plug in some points



2. y=2x-3

Solved by pluggable solver: Graphing Linear Equations
In order to graph y=2%2Ax-3 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=-3

y=2%2A%28-3%29-3

y=-6-3 Multiply

y=-9 Add

So here's one point (-3,-9)




Now lets find another point

Plug in x=-2

y=2%2A%28-2%29-3

y=-4-3 Multiply

y=-7 Add

So here's another point (-2,-7). Add this to our graph





Now draw a line through these points

So this is the graph of y=2%2Ax-3 through the points (-3,-9) and (-2,-7)


So from the graph we can see that the slope is 2%2F1 (which tells us that in order to go from point to point we have to start at one point and go up 2 units and to the right 1 units to get to the next point) the y-intercept is (0,-3)and the x-intercept is (1.5,0) ,or (3%2F2,0)


We could graph this equation another way. Since b=-3 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-3).


So we have one point (0,-3)





Now since the slope is 2%2F1, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-3), we can go up 2 units



and to the right 1 units to get to our next point


Now draw a line through those points to graph y=2%2Ax-3


So this is the graph of y=2%2Ax-3 through the points (0,-3) and (1,-1)



3. y=+%28-3%2F4%29x
Since, for some reason, the same way as previous two equations were solved doesn’t work for this one, we can find a solution for y=+%28-3%2F4%29x
by finding a line by slope and one point.
let point be (0,0) since b=0 and
slope -%283%2F4%29

Solved by pluggable solver: FIND a line by slope and one point

What we know about the line whose equation we are trying to find out:

  • it goes through point (0, 0)

  • it has a slope of -0.75



First, let's draw a diagram of the coordinate system with point (0, 0) plotted with a little blue dot:



Write this down: the formula for the equation, given point x%5B1%5D%2C+y%5B1%5D and intercept a, is

y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29 (see a paragraph below explaining why this formula is correct)

Given that a=-0.75, and system%28+x%5B1%5D+=+0%2C+y%5B1%5D+=+0+%29+, we have the equation of the line:

y=-0.75%2Ax+%2B+0

Explanation: Why did we use formula y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29 ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (x%5B1%5D, y%5B1%5D) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (x%5B1%5D, y%5B1%5D): y%5B1%5D+=+a%2Ax%5B1%5D%2Bb Here, we know a, x%5B1%5D, and y%5B1%5D, and do not know b. It is easy to find out: b=y%5B1%5D-a%2Ax%5B1%5D. So, then, the equation of the line is: +y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+.

Here's the graph: