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lord [1]
3 years ago
11

The graph of a linear equation passes through the points (-4,1) and (4,6) HELP!

Mathematics
1 answer:
umka21 [38]3 years ago
8 0

Answer:

a) (0, 3.5)

b) (12, 11)

Step-by-step explanation:

The points through which the graph of the linear equation passes are;

(-4, 1) and (4, 6)

The slope of the equation of a straight line passing through points (x₁, y₁), and (x₂, y₂), 'm', is given as follows;

Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}

∴ The slope of the equation, m = (6 - 1)/(4 - (-4)) = 5/8 = 0.625

The equation of th line in point and slope form is therefore;

y - 1 = 0.625·(x - (-4))

∴ y = 0.625·(x - (-4)) + 1 = 0.625·x + 3.5

y = 0.625·x + 3.5

Therefore;

a) When x = 0, y = 0.625 × 0 + 3.5 = 3.5

∴ The point (0, 3.5) is a solution

b) When x = 12, we have, y = 0.625 × 12 + 3.5 = 11

∴ The point (12, 11) is a solution

However;

c) When x = 8, we have, y = 0.625 × 8 + 3.5 = 8.5

∴ The point (8, 5) is not a solution

d) When x = -6, we have, y = 0.625 × (-6) + 3.5 = -0.25

∴ The point (-6, 0) is not a solution

Therefore;

The points which are solutions are;

(0, 3.5) and (12, 11)

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Which graph represents the function f(x)=
zhenek [66]

Step-by-step explanation:

you don't show us the choices.

anyway, the real graph must be similar to the one you are showing, as it goes to - and + infinity for x = 2.

because the denominator "x-2" will be 0 for x = 2.

but the horizontal limits are both y = +3 (and not 0).

because (3x-2)/(x-2) goes more and more to 3/1 the larger (or smaller in the - direction) x gets.

7 0
2 years ago
How can we find the measure of an exterior angle if we know the measurement of an interior angle
Alik [6]

Step-by-step explanation:

Put the interior angle equal to 180.


It would look something like this:

x+45=180

-45     -45

180-45= 135 so the exterior angle would be 135!

3 0
3 years ago
Let sugar be the explanatory variable and calories be the response variable; which scenario best describes ŷ = 57 + 2.5x?
algol13

Answer: Choice E)

The amount of calories in fruit juice increases by 2.5 for every one gram of sugar. The calorie amount estimated by this model is 57 if there are zero grams of sugar.

=============================================================

Explanation:

x = amount of sugar (in grams)

y = number of calories in the juice

ŷ = estimate of y, so its the estimate of calories in the juice

The regression equation rearranges to ŷ = 2.5x + 57

This is in the form y = mx+b where m = 2.5 is the slope and b = 57 is the y intercept.

The slope tells us what the rate of change is. Specifically, it tells us how much the amount of calories (y) is going up each time the amount of sugar (x) goes up. Each time x goes up by 1, y goes up by 2.5

The y intercept 57 is the starting or initial amount of calories. If you have 0 grams of sugar, the lowest amount of sugar possible, then you start off with 57 calories. We can see this by plugging x = 0 into ŷ = 2.5x + 57 (you should get ŷ = 57). Visually, the y intercept is where the line crosses the y axis.

All of these facts point to choice E as the final answer.

6 0
3 years ago
Read 2 more answers
Karen had 200 after spending y pesos on a notebook,she bought 4 colored pens with the rest of her money,what was the price of ea
pickupchik [31]

Answer:

<u>30 pesos</u>

Step-by-step explanation:

<u>Given</u>

  • Had 200 pesos originally
  • spends 'y' pesos on a notebook
  • Bought 4 colored pens with the rest of the money

<u>Solving</u>

  • Let money of the pen = x, money of notebook = y
  • 4x + y = 200
  • 4x + 80 = 200
  • 4x = 120
  • x = <u>30 pesos</u>
8 0
2 years ago
What is the slope of the line through (-3, 3) and (-1, -1)?
Vladimir79 [104]

Answer:

The slope is -2

Step-by-step explanation:

To find the slope, we can use the slope formula

m = ( y2-y1)/(x2-x1)

    = (-1 -3)/(-1 - -3)

   = ( -1-3)/(-1+3)

   = -4/2

   = -2

The slope is -2

3 0
2 years ago
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