Slope??? Linear equation??? Plots???

Question

1> Find a equation of the line containing the given pair of points (3,1) and (9,3)

What is the equation of the line? y= ?

2> How can you graph the linear equation x=y+3 on a grid?

3> Find the slope, if it exists y= -7+4

m= ???

Answer 1

general equasion of a line is y= mx+b, where m = slope and b= intercept.

slope m = (y2-y1)/(x2-x1) = 2/6 = 1/3

intercept = 0

equasion   y= 1/3 * X + 0 or y= 1/3  x

2) graph by assigning values to y and calculating x

    will need 2 points but  3 is better - can catch any errors cause they need to all be on a straight line

y= - 7 + 4  or Y = -3 which is a horizontal line so slope is non existant

Answer 2

y=mx +b

m = slope

b = y-intercept

1.  Find the slope

(Y2-Y1) / (X2-X1)

3-1/9-3 = 2/6 = 1/3



y = 1/3x

2. Set up the equation in the y=mx+b format

x = y +3

-3       -3

x-3 = y or y =x-3

The y-intercept is (0,-3) and the slope is 1 (up 1 right 1)

3. the equation must be in y = mx+b format. There is no x variable in this equation, therefore the slope is 0. You can also combined like terms (-7 and +4 to get -3 as the y-intercept).

If you have questions or you aren't sure about something ask for help. You are probably not the only one that is having trouble. Good luck!  

  

Answer 3

1.The equation of the line is

y=mx+b  

where y and x can be found from one of the points (3,1) or (9,3) but both x and y must come from the same point.

m is the slope

b is the y-intercept

so you need to find m and b and plug them back in... here's how...

a) find m

m=(y2-y1)/(x2-x1)  where the y and x values correspond to the first and second points... so

m=(3-1)/(9-3)  so

m=2/6 or 1/3

b) find b

so plug in m and one of the points (i'll use (3,1)) and solve to find b

y=mx+b

1=(1/3)*(3)+b

1=1+b

so b=0

Next...

2) you would graph x=y+3 on a grid by plugging in values for x or y and using the equation to find the other... here are some examples.

for y=0

x=0+3  so x=3  ----> now you have point (3,0)

for y=1

x=1+3  so x=4 -----> now you have point (4,1)

for y=2

x=2+3  so x=5  ----> now you have point (5,2)

continue this process to find the points and then plot them

3)The slope for y=-7+4  

this simplifies to y=-3 and if you put this in the form of this equation

y=mx+b

you get y=0*x+(-3)

so the slope is 0 because the value of y always stays the same for any value of x.

Hope this helps :-)

Answer 4

1. y = mx + b, where m = slope and b = y-intercept

Slope = (3-1)/(9-3) = 2/6 = 1/3

To find the y-intercept, use one of the points:

1 = (1/3)(3) + b

1 = 1 + b

0 = b, so the y-intercept is 0

The final equation is : y = 3x

Check:

3 = (1/3)(9)

3 = 3, so it checks.

2. Change it around so it fits the mx+b equation:

x - 3 = y

So the slope is 1, and the y-intercept is -3

So on a graph, mark the point (0,-3). Since the slope is 1, you'll move up 1 for every 1 you move over, so the next point would be (1, -2). Connect these 2 points and you'll see the formation of the line.

3. That's just a point? There's no x in the equation.... the point is y = -3, and there's no slope to a horizontal line, so, no, it doesn't exist in the equation that you gave.