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What is an equation of the line that passes through the points (6,5) and (7,7)

User Pura
by
7.3k points

2 Answers

4 votes

Answer:

The slope of the line is m = 2.

The y-intercept is (0,7).

The equation of the line in the slope-intercept form is y = 2 x - 7.

Explanation:

The slope of a line passing through two points
P = \left(x_(1), y_(1)\right) and
Q = \left(x_(2), y_(2)\right)

is given by
m=(y_(2)-y_(1) )/(x_(2) -x_(1) )

We have that
x_(1) = 6 ,
y_(1) = 5y , and
y_(2) =7.

Plug the given values into the formula for a slope:
m=(7-5)/(7-6) =2.

Now, the y-intercept is
b=y_(1) -mx_(1) (or
b =y_(2) -mx_(2), the result is the same).


b=5-(2)*(6)=-7

Finally, the equation of the line can be written in the form
y=b+mx:


y=2x-7

User Noj
by
8.0k points
8 votes

Answer:


  • \Large\boxed{\sf{y=2x-7}}

Explanation:

The slope formula is used to find the equation of the line that passes through the points in this problem.

SLOPE FORMULA:


\Longrightarrow: \sf{(y_2-y_1)/(x_2-x_1)=(RISE)/(RUN) }

  • y₂=7
  • y₁=5
  • x₂=7
  • x₁=6


\Longrightarrow: \sf{(7-5)/(7-6)=(2)/(1)=2 }

Use the slope-intercept form.

SLOPE-INTERCEPT FORM:


\Longrightarrow: \sf{Y=MX+B}


\Longrightarrow: \text{The M represents the


\Longrightarrow: \text{The B represents the

y=2x-7

  • Therefore, the slope is 2 and the y-intercept is 7.
  • The correct answer is y=2x-7.

I hope this helps. Let me know if you have any questions.

User Darkgaze
by
8.7k points

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