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Sagot :
Answer:
y = - 5/2 x + 1/ 2
Explanation:
A linear equation in slope-intercept form is given by
[tex]y=mx+b[/tex]where m = slope and b = y-intercept.
Now in our case, we are told that our equation has a slope of -5/2. This means m = -5/2 and so we have
[tex]y=-\frac{5}{2}x+b[/tex]Furthermore, we are also told that the line defined by this equation passes through (-1, 3). This means that our equation must satisfy x = -1 when y = 3.
Putting x = -1 and y = 3 into the above equation gives
[tex]3=-\frac{5}{2}(-1)+b[/tex]Our goal now is to solve for b.
The negative signs on the right-hand side cancel to give
[tex]3=\frac{5}{2}+b[/tex]subtracting 5/2 from both sides gives
[tex]3-\frac{5}{2}=\frac{5}{2}+b-\frac{5}{2}[/tex][tex]3-\frac{5}{2}=b[/tex]Since 3 - 5/2 = 1/2, the above becomes
[tex]b=\frac{1}{2}[/tex]Hence, the equation of our line in slope-intercept form is
[tex]\boxed{y=-\frac{5}{2}x+\frac{1}{2}\text{.}}[/tex]
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