Question

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

Answer 1

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`

Answer 2

• 
  `\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.