Can anyone describe the steps to solving these equations?

Question

To those who answer both, I'll give maximum star rating and best answer.

1st problem - find the slope, slope intercept form, stabndard form and two points on the line of an equation with an x int. of 4 and a y int. of -1.

2nd problem-- find the standard form, slope-intercept form, slope and two points on the line of an equation with an x int. of -3 and a y intercept of "none"

Answer 1

Hello

1) If the x-int is 4 and the y-int is -1. Then we have the points (4,0) and (0,-1).

So lets find the slope: (y2-y1) / (x2-x1). Thus the slope is -1/ -4 = (1/4).

So we have y = mx +b (slope intercept form).
Plug in one of the order pairs above to get:
0 = (1/4)4 + b. Thus we have b = -1,

So the slope intercept form is y = (1/4) x -1

So the standard form would be: (-1/4) x + y = 1.

B). If the x-int is -3 then we have the point (-3,0) and if there is no y int then we know that this is a vertical line.

Thus the equation is x = -3 is the slope intercept form

Standard form would be the same or you could say x + 0y = -3.

Two points on the line could be (-3, 0) and (-3,1).

Hope this helps

Answer 2

x/a+y/b =1 is the intercept form of the equation of a straight line, where a is the x-intercept and b is the y-intercept.
Hence the equation in this form is x/4 + y/-1 = 1.

Multiplying by 4 we get x -4y =4 or
y = x/4 -1 which is the slope intercept form. The slope is 1/4 and the y-intercept is -1.

Standard form would be x/4 -y -1 = 0
two points on the line would be ((4,0) and (0,-1).

-----------------------------------------------------------------------------
If there is no y-intercept the equation is simply x= -3. It is a vertical line parallel to the y-axis and passing through the point (-3,0).

Standard form is x +3 = 0
No slope intercept form because slope is undefined.
Two points on the line would be (-3,6) and (-3,50)

Answer 3

1. The slope of this is rise (1) over run (4). So y=mx+b yields:
y = .25x - 1

Two points can be (1,-.75) and (2,-.5)

2. Since this line does not intersect the y-axis, it must be perfectly vertical, so the slope is undefined. y = mx + b does not work in this situation because m is undefined. The equation is x = -3.
All the points are given by (-3,y), for all real y.

Answer 4

standard forms
a) slope - intercept with slope and intercept
y = mx + c ----- eqn (1)
where m = slope, c = y- intercept

b) point slope form with two points(x1,y1), (x2,y2)
(y - y1) = m(x - x1) ------- eqn(2)
where slope, m = (y2 -y1)/(x2 - x1)

c) standard form with x and y intercpts
x/a + y/b = 1 -------- eqn(3)
where a = x-intercept
b = y - intercept
1)
x-intercept = a = 4
y-intercept = b = -1
substituting in eqn (3)
x/4 + y/(-1) = 1
multiplying with 4
x - 4y = 4
x - 4y - 4 =0

2) a = -3
b = 0
x/-3 + y/(0) = 1
this is a line with undefined slope
line with undefined slope is vertical line parallel to y - axis
so the the equation is
x/(-3) = 1
multiplying with -3
x = - 3
x+ 3 = 0

Answer 5

1)

(x,y)

y = mx + b

(4, 0), (0, -1)

0 - (-1)
---------
4 - 0

m = 1/4 <-------------------------- slope

(4, 0)

0 = 1/4 (4) + b

0 = 1 + b

b = -1

y = (1/4)x - 1 <------------------------- slope intercept form

ax + by = c

(1/4)x - 1 - y = 0

x - 4 - 4y = 0

x - 4y = 4 <-------------------------- standard form