Question

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

Answer 1

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.

Step-by-step 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  $m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

We have that $x_{1} = 6$ , $y_{1} = 5y$ , and $y_{2} =7.$

Plug the given values into the formula for a slope: $m=\frac{7-5}{7-6} =2$.

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 $y=b+mx$:

$y=2x-7$

Answer 2

Answer:

• $\Large\boxed{\sf{y=2x-7}}$

Step-by-step explanation:

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

SLOPE FORMULA:

$\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{RISE}{RUN} }$

• y₂=7
• y₁=5
• x₂=7
• x₁=6

$\Longrightarrow: \sf{\dfrac{7-5}{7-6}=\dfrac{2}{1}=2 }$

Use the slope-intercept form.

SLOPE-INTERCEPT FORM:

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

$\Longrightarrow: \text{The M represents the "slope".}$

$\Longrightarrow: \text{The B represents the "y-intercept".}$

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.