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uysha [10]
3 years ago
6

The linear function f i with values f(-1) = 10 and f(5) = -1 is f(x)

Mathematics
1 answer:
zhenek [66]3 years ago
3 0
Answer:

Use the two points to compute the slope, m, then use one of the points in the form <span>y=m<span>(x)</span>+b</span> to find the value of b.

Explanation:

The equation for the slope, m, of a line is:

<span>m=<span><span><span>y1</span>−<span>y0</span></span><span><span>x1</span>−<span>x0</span></span></span> [1]</span>

The equation <span><span>f<span>(2)</span></span>=−1</span> tells us that <span><span>x0</span>=2and<span>y0</span>=−1</span>; substitute this into equation [1]:

<span>m=<span><span><span>y1</span>−−1</span><span><span>x1</span>−2</span></span> [2]</span>

The equation <span><span>f<span>(5)</span></span>=4</span> tells us that <span><span>x1</span>=5and<span>y1</span>=4</span>; substitute this into equation [2]:

<span>m=<span><span>4−−1</span><span>5−2</span></span> [3]</span>

<span>m=<span>53</span></span>

Substitute <span>53</span> for m into the equation <span>y=m<span>(x)</span>+b</span>

<span>y=<span>53</span>x+b [4]</span>

Substitute 2 for x and -1 for y and the solve for b:

<span>−1=<span>53</span><span>(2)</span>+b</span>

<span>b=−<span>133</span></span>

Substitute <span>−<span>133</span></span> for b in equation [4]:

<span>y=<span>53</span>x−<span>133</span> [5]</span>

Check:

<span>−1=<span>53</span><span>(2)</span>−<span>133</span></span>
<span>4=<span>53</span><span>(5)</span>−<span>133</span></span>

<span>−1=−1</span>
<span>4=<span>4</span></span>

<span><span>
</span></span>

<span><span>Hope this helps </span></span>

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It should be noted that the relationship is not linear based on the information illustrated as the difference between the numbers aren't the same.

<h3>How to illustrate the information?</h3>

It should be noted that an equation is simply used to illustrate and express the relationship between the variables.

It should be noted that for the relationship to be linear, it's essential that they've the same relationship between them.

When x = 1, y = 4.5. The

When x = 2, y = 6.5

When x = 3, y = 8.5

When x = 4 y = 11.5

It should be noted that there's a difference of 2 at first but between 3 and 4, there is. a difference of 3.

Therefore, the relationship is not linear.

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brainly.com/question/2972832

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Answer: \left \{ {{y\leq -\frac{5}{3}x + \frac{11}{3}} \atop {y < 8}} \right

<u>Step-by-step explanation:</u>

(1, 2) and (4, -3)

First, find the slope (m): \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

m = \frac{-3-2}{4-1}

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Next, choose ONE of the points and input the point and slope into the Point-Slope formula: y - y₁ = m(x - x₁)

y - 2 = -\frac{5}{3}(x - 1)

y - 2 = -\frac{5}{3}x + \frac{5}{3}

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Then, determine which inequality symbol will result in (-2, 8) being False (since it is not a solution):

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8 ___ -\frac{5}{3}(-2) + \frac{11}{3}

8 ___ \frac{1}{3}

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so ≤ makes the statement False

⇒ y ≤ -\frac{5}{3}x + \frac{11}{3}

****************************************************************

If you need a "system" of inequalities, then you need another equation.

There are infinite possibilities. Graph the points to see what works.  

y < 8   or  x > -2 are two examples.


---> I just realized that the system can be simpler than what I did above:

\left \{ {{x>-2} \atop {y < 8}} \right



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