Question

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

Answer 1

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:

• m is the slope
• (x₁,y₁) is a point on the line

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!