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>
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<span><span>Hope this helps </span></span>
it is a rational number.