Write an equation of the line that passes through a pair of points:

a. y = x + 3
b. y = x-3
C. y = -x + 2
d. y=-x-2

Answer choice B

Step-by-step explanation:

This line passes through the points (4,1) and (5,2). The formula for a line in slope intercept form is y=mx+b, where m represents the slope and b represents the y coordinate of the y intercept. The slope can be found by comparing the rise with the run. When the line goes from (4,1) to (5,2), it rises 1 unit and runs (goes to the right) 1 unit. 1/1=1, so the slope of this line is 1. The y intercept can be seen to be at (0,-3), meaning that b=-3. Therefore, the formula is y=x-3 or answer choice B. Hope this helps!

B

Step-by-step explanation:

Our equation should be in the form y = mx + b, where m is the slope and b is the y-intercept.

The slope is found by taking any two points on the line and finding the change/difference in the y-coordinates and then dividing that by the change/difference in the x-coordinates.

Here, we're given two points: (4, 1) and (5, 2). Our slope will then be:

The slope is 1, so m = 1.

The y-intercept is the place where the graph intersects with the y-axis. Looking on the graph, that point is (0, -3), so the y-intercept is b - 3.

Plug these values into the equation:

y = mx + b

y = 1 * x + (-3)

y = x - 3

The answer is B.

The given statements are arranged in the numbers starting from 1 to 6 and are highlighted with red color in the provided attachment.

Statement 1 - FALSE

Statement 2 - FALSE

Statement 3 - TRUE

Statement 4 - TRUE

Statement 5 - TRUE

Statement 6- FALSE

Explanation:

(1) Due to the tidal effect, the level of water bodies on earth increases due to the gravitational pull of the moon. It bulges out on both sides when high tide occurs in any particular place.

(2) Earth's gravity pulls any object that moves against its direction. The gravity creates an obstruction for the spacecraft to fly and affects the speed of the spacecraft.

(3) Our solar system, including the sun, planets all revolves around the center of the galaxy and the velocity at which they are moving is about 828,000 km/hr on an average.

(4) Gravity plays an important role in sticking the gases near the surface of the earth. In the absence of gravity, all these gases would escape into the outer atmosphere and there will be no atmosphere on earth.

(5) The size of the planet Jupiter is almost 11 times larger than the earth's size and so the mass of Jupiter also is comparatively very high. Thus, the mass on earth is lesser than the mass on Jupiter.

(6) The mass of an object is the product of the velocity and density of the object and this can be easily derived from the density formula.