Write the equation of the line that passes through the points (3,5) and (6,2), giventhat the point slope form is y 3 - 10.30 - 5), in slope-intercept form.

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PearlaG603596 PearlaG603596 · Answer 1 · 2022-10-25T23:36:05+02:00

[tex]\begin{gathered} (3,5) \\ (6,2) \end{gathered}[/tex]

the general equatin of a line is

[tex]y=mx+b[/tex]

where m is the slope and b the y-intercept

firs find the slope using

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

where (x2,y2) is a right point from (x1,y1)

on this case (x2,y2) is (6,2)

so replacing

[tex]\begin{gathered} m=\frac{2-5}{6-3} \\ \\ m=\frac{-3}{3}=-1 \end{gathered}[/tex]

the slope is one

now to calculate b we replace the slope and a point and solve b

i will use (3,5)

[tex]\begin{gathered} (5)=(-1)(3)+b \\ 5=-3+b \\ b=5+3 \\ b=8 \end{gathered}[/tex]

now replacing the slope and b, the equation of the line is

[tex]y=-x+8[/tex]