Can you do this co-ordinate geometry?

Question

How would i determine the slope of the line with the equation:
5x-y=8

find the axes intercepts of the line with equation 3x-4y=-12

find b if (b,3) lies on the line with equation 2y-3x=15

Anything is appreciated and if anyone could show how they got the answer. Thanks in advance.

Answer 1

1. 5x-y= 8
y = 5x-8
so slope = 5

2. x intercept can b calculated when y=0
3x-4y= -12
3x = -12
x= -4
so x intercept is (-4,0)

y intercept can b calculated when x = 0
-4y= -12
y=3
so y intercept is (0,3)

3. if (b,3) lies on this line
substituting we get
2( 3) - 3(b) = 15
6-3b=15
-3b=9
b=-3

Answer 2

5x-y= 8
y = 5x-8
Put in form Y = mX + c
where m = 5
:> slope = 5

the axes intercepts of the line with equation 3x-4y=-12
at x- axis y = 0
3x-4(0) = -12
3x = -12
x = -4 (-4 , 0)

at y- axis x = 0
3(0) -4y = -12
-4y = -12
x = 3 (3 , 0)

b if (b,3) lies on the line with equation 2y-3x=15
2( 3) - 3(b) = 15
6-3b = 15
-3b = 9
b = -3

Answer 3

1. Change the orientation of the equation so you get
y = 5x - 8. Using the formula y = mx + b (m being the slope), you can get the slope to be 5.

2. With this one, all you need to do is plug in 0 for the x to get the y axis intercept, and plug in 0 for y to get the x axis intercept. Doing this, I get (4,0) for the y-axis intercept, and (0,-3) for the x-axis intercept.

3. This is a lot like 2. All we have to do is plug in 3 for y, and solve for x (or b in this problem). Doing this, I get b = 3.

Answer 4

5x-y=8, in y=mx+b format is (subtract 5x from both sides)
-y = -5x + 8 (then divide both sides by -1)
y = 5x - 8. So, m (your slope) is 5.

axes intercepts:
for the point hitting the y axis, x is zero. So,
3x - 4y = -12
3(0) - 4y = -12
-4y = -12 (divide by -4)
y = 3. So it's at (0,3).
for the one on the x axis, y is zero. So,
3x - 4(0) = -12
3x = -12 (divide by 3)
x = -4. So it's at (-4, 0)

for the line with (b,3), plug 3 in for your y value:
2(3) - 3x = 15
6 - 3x = 15 (subtract 6)
- 3x = 9 (divide by -3)
x = -3 .

Answer 5

some super books for those matters that I enjoyed: larger Algebra : corridor and Knight Geometry: For uncomplicated Euclidean geometry, reckoning on how deep you pick to pass, Euclid's factors is the authoritative source. Trigonometry and Coordinate Geometry - no longer something comes on the threshold of S L Loney's classics.

Answer 6

slope of 5x-y=8 is 5-- aka whatever coefficient is in front of x as long as the constsnt next to y is 1.

to find axes intercepts set, one at a time, x and y equal to 0

to find b plug in 3 for the y value and b for your x value and yo uwill get b

Answer 7

Question 1
y = 5x - 8
slope = 5

Question 2
(0,3) and (- 4,0)

Question 3
6 - 3b = 15
3b = - 9
b = - 3