Question

What is the point-slope form for the equation of the line
connecting (-4,1) and (4,7).

Answer 1

Equations using the point slope form

Given a line connecting $(-4,1)$ and $(4,7)$

1. Find the slope of the line

To do such, we use the formula of a slope

`(\Delta y)/(\Delta x) = (y_(2) - y_(1))/(x_(2) - x_(1))`

Let:
`x_(1) &=& -4 \,; x_(2) &=& 4 \\ y_(1) &=& 1 \,; y_(2) &=& 7`

2. Subtitute them into the formula

`(y_(2) - y_(1))/(x_(2) - x_(1)) = (7 - 1)/(4 - (-4)) = (6)/(8) = (3)/(4)`

The slope ($m$) is $\dfrac{3}{4}$

3. The equation in the point-slope form

$y - y_{1} = m(x - x_{1})$

4. Substitute into the formula

`y - (1) &=& (3)/(4)(x- (-4)) \\ y &=& (3x)/(4) + 4`

Therefore the answer $y = \dfrac{3x}{4} + 4$