Write an equation of the line in point-slope form that passes through the given points. (2,6) and (3,10)

Question

asked Apr 28, 2024 215k views

1 Answer

Superdrac · Answer 1 · 2024-05-02T22:49:48+0000

Hi there!

$\small\textbf{ANSWER:}$

$\bullet\qquad\sf{y-6=4(x-2)}$

$\small\textbf{EXPLANATION:}$

We are asked to find the equation of the line in point-slope form.

Use the point-slope formula:

$\bullet\quad\bold{y-y_1=m(x-x_1)}$

where:

We have a point, but we don't have the slope. To find the slope, we will use this formula:

$\bullet\quad\bold{m=\cfrac{y_2-y_1}{x_2-x_1}}$

Substitute the values.

$\sf{m=\cfrac{10-6}{3-2}}$

$\sf{m=\cfrac{4}{1}}$

$\sf{m=4}$

Therefore, the slope is 4.

Now we have both the point and the slope, so we substitute the values into the point-slope formula.

Reminder: The formula is:

$\large\boldsymbol{\rm{y-y_1=m(x-x_1)}}$

Substitute the values.

$\large\boldsymbol{\rm{y-6=4(x-2)}}$

This is our point-slope equation.

Best wishes!