Find the equation of the line that goes through (3, 0) and (0, -6)?

Question

Please show the work so I can learn instead of just getting the answer.

Thanks.

Answer 1

Step one: Find the slope.

Slope is (y2-y1) / (x2 - x1) = -6-0 / 0-3 = -6 / -3 = 2

Now, find the y-intercept.

Since one of the points is (0, -6) you know that y is -6 when x is 0.

So, using the equation of a line:

y = mx + b where "m" is the slope and "b" is the y intercept,

The equation is:

y = 2x-6

You can check by plugging your points in to see if they work.

Regards,

Mysstere

Answer 2

There are several ways to solve this problem. The most ease idea is:

a) The equation of a line has the form: y = ax + b
b) If a point belongs to the line it must verify the identity, that is, if the line goes through (2,5)(for example) we put 2 in place of x and 5 in place of y ... getting... 5=2a+b ... an equation.

Now let use the proceeding to this question:

Put the point (3,0) in the equation: 0=3a + b
Put the point (0,-6) in the equation: -6 =0a + b

Now we have two equations
3a + b = 0
0a + b = -6... just solve the system of equations... b= -6 and a=2

After finding a and b we can write the equation of the line:
y= 2x -6

This proceeding may be applied to whatever two given points.

Answer 3

Draw a picture. y = mx +b is the canonical form for a line. When x = 0, y = -6 (0,-6) so -6 = m*0 + b. So b = -6. When y = 0, x = 3 (3,0) so 0 = m*3 + (-6). Thus, m = 2. So you have y = mx +b = 2x - 6.

Answer 4

The slope is 0--6/3-0=2 and the y-intercept is -6 so the equation is y=2x-6

Answer 5

two good answers here already (esp. myssteee's), I'll just add if you draw the two points on graph paper, you will see the gradient or slope, which is often called m

as in y=mx+c

if m = 2 then the line is steep, and if you go along 1 unit on the x axis then you go up 2 on the y axis.

and c is where the line crosses (intercepts the x axis).

remember the notation is to write (x,y) so your points are

x=3 & y=0 & the second point is x=0 & y= -6

and x is the horizontal axis, and y is the vertical.

anyway enough babbling.

goodluck

T

Answer 6

1st find the slope:
m=(y2-y1)/(x2-x1)=(-6-0)/(0-3)=-6/(-3)=2
y=2x+b
choose either point
-6=2*0+b
b=-6 so
y=2x-6

check with the other point
0=2*3-6=0

Answer 7

you should put your points coords in this formula:
(y2-y1)/(x2-x1)=(y-y1)/(x-x1)
it means tangant every (x,y) and one of your points should be equal to tangant of your 2 points
it gives you a line equation which goes from those 2 points
which is: y=x/2+3