Question

Write an equation in point-slope form of the line that passes through the two given points. Use the first point to write the equation (-1, -5) and (3, 2)

Answer 1

The equation in point-slope form of the line is:

`y-\left(-5\right)=(7)/(4)\left(x-\left(-1\right)\right)`

Explanation:

Given the points

• (-1, -5)

• (3, 2)

`\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-1,\:-5\right),\:\left(x_2,\:y_2\right)=\left(3,\:2\right)`

`m=(2-\left(-5\right))/(3-\left(-1\right))`

`m=(7)/(4)`

As the point-slope form is defined as

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

where m is the slope.

substituting the values m=7/4 and the first point (-1, -5)

`y-\left(-5\right)=(7)/(4)\left(x-\left(-1\right)\right)`

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

`y-\left(-5\right)=(7)/(4)\left(x-\left(-1\right)\right)`