Question

Which line passes through the points (3,4) and (8,-1)?

Answer 1

Answer:

The equation of a line is typically written as y=mx+b (1)where m is the slope and b is the y-intercept. If you know two points that a line passes through than we can find the equation as first find the slope

Slope=m=y2-y1/x2-x1=(-1-4)/8-3)=-5/5=-1

For y-intercept put the value of any point and slope in equation (1)

y=mx+b

For point (3,4)

4=(-1)3+b

4=-3+b

b=4+3

b=7 (y-intercept)

Put the value of m and y-intercept in eq(1) as

y=mx+b

y=-x+7

x+y=7 (Equation of the required line)

Step-by-step explanation:

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Answer 2

SOLUTION

TO DETERMINE

The equation of the line passes through the points (3,4) and (8,-1)

EVALUATION

Here the given points are (3,4) and (8,-1)

Hence the required equation of the line is

$\displaystyle \sf{ \frac{y - 4}{x - 3} = \frac{ - 1 - 4}{8 - 3} }$

$\displaystyle \sf{ \implies \frac{y - 4}{x - 3} = \frac{ - 5}{5} }$

$\displaystyle \sf{ \implies \frac{y - 4}{x - 3} = - 1}$

$\displaystyle \sf{ \implies y - 4 = - x + 3}$

$\displaystyle \sf{ \implies x + y - 7= 0}$

Hence the required equation of the line is

$\displaystyle \sf{ x + y - 7= 0}$

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