Question

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Select all the points that are on the line through LaTeX: (0,5)( 0 , 5 ) and LaTeX: (2,8)( 2 , 8 ). Group of answer choices LaTeX: (4,11) ( 4 , 11 ) LaTeX: (5,10) ( 5 , 10 ) LaTeX: (6,14) ( 6 , 14 ) LaTeX: (30,50) ( 30 , 50 ) LaTeX: (40,60)​

Answer 1

Answer:

(4,11), (6,14), (30,50)

Step-by-step explanation:

Since you are given two points, you can find the slope of the line and also the equation of the line. At first, it seemed like you could just use patterns and logic. One point on the line is (0,5) (this is the y-intercept and later we'll use this information) The next given point is (2,8) In order to get from (0,5) to (2,8) you must go up 3 and over (to the right) 2. Looking over the answers, we can see immediately that the next point "up 3 and over 2" is at (4, 11) which is one of the answer choices. But also, if you go once more "up 3 and over 2" you will land on (6,14) which is also an answer choice.

(5,10) CANNOT be an answer because in between the points (0,5), (2,8), (4,11), and (6,14) the line does not cross at an integer value. For example at x = 1 the y-value will be 6.5

However, we may as well write an equation for the line in order to check the points (30,50) and (40,60) The equation of the line using y=mx+b (this is called slope-intercept formula) is

y = (3/2)x + 5

We know this because that "up 3 and over 2" we were using is actually the slope, m, in the equation in front of the x, written as a fraction 3/2. The 5 is the y-intercept which we were given in the point (0,5)

Now if (30,50) or (40,60) are on the line then they will satisfy this equation.

y = (3/2)x + 5 when x = 30

y = (3/2)(30) + 5

y = 45 + 5

y = 50 so (30, 50) is also on this line

y = (3/2)x +5

y = (3/2)(40) + 5

y = 60 + 5

y = 65

So (40, 60) IS NOT on the line.

Alternatively you could use only slope formula to calculate the slope with the two given points (which you will find is 3/2. And then check each potential answer with one given point in the slope formula, keeping any point that also yields a slope of 3/2 and discarding any answers that do not give a slope of 3/2

Answer 2

The coordinate points that are on the line are (4, 11), (6, 14), and (30 50)

Equation of a line

The equation of a line in slope-intercept form is expressed as y = mx + b

Given the coordinate points (0, 5) and (2, 8), first, we need to find the equation of the line passing through this point.

Slope and intercept of a line

Get the slope of the equation:

$m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{8-5}{2-0}\\ m=\frac{3}{2}\\ m=1.5$

The y-intercept is the point where x = 0. From the given coordinates, you can see that b = 5.

Get the required equation:

Recall that y = mx + b. On substituting;

y = 1.5x + 5

Next is to check which of the points listed are on the line.

For the coordinate (4,11).

If x = 4

y = 1.5(4) + 5

y = 6 + 5

y = 11

Therefore (4, 11) is on the line y = 1.5x + 5

For the coordinate (5,10).

If x = 5

y = 1.5(5) + 5

y = 7.5 + 5

y = 12.5

Therefore (5, 10) is NOT on the line y = 1.5x + 5

For the coordinate (6,14).

If x = 4

y = 1.5(6) + 5

y = 9 + 5

y = 14

Therefore (6, 14) is on the line y = 1.5x + 5

For the coordinate (30,50).

If x = 30

y = 1.5(30) + 5

y = 45 + 5

y = 50

Therefore (30, 50) is on the line y = 1.5x + 5

For the coordinate (40,60).

If x = 40

y = 1.5(40) + 5

y = 60 + 5

y = 65

Therefore (40, 65) is on NOT the line y = 1.5x + 5

Hence the coordinate points that are on the line are (4, 11), (6, 14), and (30 50).

Learn more on the equation of a line here: brainly.com/question/13763238