Question

What is the equation, in point-slope form, for a line that goes through ​(2, −6)​ and has a slope of ​−3/4​ ?

Answer 1

Hi there!

The question is asking us to write the equation, in point-slope form, for a line that goes through ​(2, -6)​ with a slope of ​−3/4​.

Point-slope is:

`\sf{y-y_1=m(x-x_1)}`

Plug in all the data:

`\sf{y-(-6)=-(3)/(4)(x-2)}`

Simplify the left side:

`\sf{y+6=-(3)/(4)(x-2)}`

Therefore, this is the equation.

Have a fantastic day!

Answer 2

`\displaystyle{y+6=-(3)/(4)\left(x-2\right)}`

Explanation:

The point-slope equation is in the form of:

`\displaystyle{y-y_1=m(x-x_1)}`

Given that the line goes through (2, -6). Therefore (x₁, y₁) = (2, -6). We are also given the slope (m) of -3/4. By substituting in the values, we have:

`\displaystyle{y-\left(-6\right)=-(3)/(4)\left(x-2\right)}\\\\\displaystyle{y+6=-(3)/(4)\left(x-2\right)}`

Therefore the equation, in point-slope form, is:

`\displaystyle{y+6=-(3)/(4)\left(x-2\right)}`