Question

I really need help with this question.

Write the equation of the line that pass through the points below. Write your answer in Point-Slope Form or Slope-Intercept Form. Do NOT use any spaces in your answer.


(2, 17), (4, 7)


Equation:

Answer 1

Please check the explanation.

Explanation:

Given the points

• (2, 17)

• (4, 7)

Finding the slope between (2, 17), (4, 7)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(2,\:17\right),\:\left(x_2,\:y_2\right)=\left(4,\:7\right)`

`m=(7-17)/(4-2)`

`m=-5`

We know the Point-Slope Form of the line equation is

`y-y_1=m\left(x-x_1\right)`

Here:

• m is the slope

• (x₁, y₁) is the point

substituting the values m = -5 and the point (2, 17) in the Point-Slope Form

`y-y_1=m\left(x-x_1\right)`

`y - 17 = -5 (x-2)`

Thus, the answer Point-Slope Form is

`y - 17 = -5 (x-2)`

It can be further simplified to write into the Slope-Intercept Form

`y - 17 = -5 (x-2)`

y-17 = -5x+10

y = -5x+10+17

y = -5x+27

Thus, the answer in the Slope-Intercept Form (y=mx+b)

y = -5x+27 ∵Slope-Intercept Form → y=mx+b