Question

(2,7),(1,-4)write an equation for the line in point slope form .Then rewrite the equation in slope intercept form

Answer 1

Let's begin by listing out the information given to us:

`\begin{gathered} (x_(1,)y_1)=(2,7) \\ (x_(2,)y_2)=(1,-4) \end{gathered}`

Let's calculate the slope

`m=(y_2-y_1)/(x_2-x_1)=(-4-7)/(1-2)=(-11)/(-1)=11`

Slope = 11

Using point slope form, we have:

`\begin{gathered} y-y_1=m(x-x_1) \\ y-y_2=m(x-x_2) \\ Using(1,-4) \\ y--4=11\left(x-1\right) \\ y+4=11x-11 \\ \text{Subtract 4 from both sides} \\ y=11x-15 \end{gathered}`

Write the equation in slope intercept form, we have:

The general formula is given by y = mx + b

Let's calculate the slope

`m=(y_2-y_1)/(x_2-x_1)=(-4-7)/(1-2)=(-11)/(-1)=11`

The general formula becomes,

y = 11x + b

To solve for b, make b the subject formula, we have:

b = y - 11x

Substitute (2, 7) into the formula

b = 7 - 11 (2) = 7 - 22 = -15

b = -15

Substitute the value of b into the formula y = 11x + b, we have:

`y=11x-15`