Finding the equation of a line.?

Question

1) Are Linear equations are equations that form a line

2)Which of the following equations has a slope of ½ and a y-intercept of -2?
y = -2x + ½

y = ½x + 2

y = ½x - 2

½x - 2y = 4

3)Write the equation of a line which contains the points (2,2) and (-3,12)

4)Which equation has a slope of 2 and contains the point (4,-4)?

5) The line y = 3x + 5 crosses the y axis at ______?

Answer 1

Hello

1) Yes - Lineral Equations are equations of lines

2) y=mx+b is the slope intercept form - (m=slope and b=y-int). So the answer is y = ½x - 2.

3) Write the equation of a line which contains the points (2,2) and (-3,12) -

First lets find the slope = 12-2 / -3-2 = 10/-5 = -2 = m

So we have y = -2x+b.
Plug in any of the 2 ordered pairs mentioned above

2 = -2(2) + b ---- thus b=6.

The equation is then y = -2x+6.

Hope this helps

4) So we have -4 = 4(2) + b. Thus means that b = -12.
Equation is y = 2x-12

5) The y-intercept is 5 thus the answer is (0,5).

Hope this helps

Answer 2

1) These equations are called "linear" because they represent straight lines in Cartesian coordinates.

2) A common form of a linear equation in the two variables x and y is y=mx+b.
In this form, the constant m will determine the slope or gradient of the line; and the constant term b will determine the point at which the line crosses the y-axis.
Therefore, y = ½x - 2 has a slope of ½ and a y-intercept of -2.

3) We find the slope using the equation
m = (y2-y1)/(x2-x1)
= is 12-2 / -3-2 = 10/-5 = -2
So plugging the slope and first point into y = mx+b gives us
2 = -2 * 2 + b
2 = -4 + b
6 = b
Our formula is y = -2x + 6.
Check the other point:
-2 * -3 + 6 = 6 + 6 = 12

4) y = mx + b
-4 = 2*4 + b
-4 = 8 + b
-12 = b
Therefore the equation is y = 2x-12

5) The line y = 3x + 5 crosses the y axis when x = 0
So y = 3*0 +5 = 5
Therefore, the line y = 3x + 5 crosses the y axis at (0,5)

Answer 3

1) Yes, hence the term LINEar, which basically means straight.

2) linear equations of the slope intercept form are like this: y = mx+b, where m is the slope, and b is your y intercept value. I don't want to do your homework. You figure that one out. =P

3) To find the slope of this line given those points, you can use the following formula:

y2-y1/x2-x1 remember coordinates are listed as follows: (x,y)

you can finish the necessary algebra, right?

4) Remember y = mx+b. Plug in the x and y values and solve for b, your y intercept.

5) This should be duh by now. Lol.

Answer 4

All linear equations graph as a straight line.

y = 1/2 x -2

Slope = (12-2)/(-3-2)= 10/-5 = -2
So y = -2x +b
2=-2(2) +b, so b = 6
Thus equation is y = -2x + 6

y= 2x+b
-4 = 2*4 + b, so b = -12
The equation is y = 2x - 12

(0,5) It crosses the y-axis when x = 0.

Answer 5

1)yes
2)y = ½x - 2
3)
(y-2)/(x-2)=(12-2)/(-3-2)
(y-2)/(x-2)=10/-5=-2/1
y-2=-2x+4
y+2x=6
4) 2/1=(y+4)/(x-4)
y+4=2x-8
y-2x=-12
5)5