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

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