Question

Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.Passing through (-4-3) and (1,2)What is the equation of the line in point-slope form?(Simplify your answer. Use integers or fractions for any numbers in the equation.)What is the equation of the line in slope-intercept form?(Simplify your answer. Use integers or fractions for any numbers in the equation.)

Answer 1

Hello!

Let's write the points here:

• A = (-4, -3)

,

• B = (1, 2)

First, we have to calculate the slope of this line, using the formula:

`\text{Slope}=(y_B-y_A)/(x_B-x_A)`

Let's replace the values in the formula:

`\text{Slope}=\frac{2_{}-(-3)_{}}{1-(-4)_{}}=(2+3)/(1+4)=(5)/(5)=1`

So, the slope of this line will be 1.

Now, let's write the equation in the point-slope form:

`y-y_(1)=m\mleft(x-x_(1)\mright)`

We can choose any point to replace in (x1, y1). I'll use point A:

`\begin{gathered} y-(-3)=1\mleft(x-(-4)\mright) \\ y+3=1(x+4) \end{gathered}`

To finish, the equation in slope-intercept form:

`y=mx+b`

Let's replace using the point B and m = 1:

`\begin{gathered} 2=1\cdot1+b \\ 2=1+b \\ 2-1=b \\ b=1 \end{gathered}`

So, the equation in the slope-intercept form is:

y = 1x +1

Answer:

• Equation in point-slope form: ,y+3=1(x+4)

,

• Equation in slope-intercept form: ,y = 1x +1