Question

What is the equation of the line that passes through the point (5,4) and has a slope of 2

Answer 1

Hello,

$y = ax + b$

We know the slope is 2 so :

$y = 2x + b$

The equation of the line that passes through the point (5,4) so :

$4 = 2 \times 5 + b$

$4 = 10 + b$

$b = 4 - 10$

$b = - 6$

The equation of the line that passes through the point (5,4) and has a slope of 2 is :

$y = 2x - 6$

Answer 2

Answer:

y = 2x - 6

Step-by-step explanation:

Most lines are written in slope-intercept form, but we can use slope-point form in situations like this.

Slope-Point Form

The formula for slope-point form is $y-y_{1}=m\left(x-x_{1}\right)$. So, we can plug in the information we have, the point and slope.

• y - 4 = 2(x - 5)

This is an equation for the line given to us. However, this form can be simplified further.

Slope-Intercept Form

Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept. To find the most simplified form of the equation we need to use the properties of equality.

First, distribute the 2

• y - 4 = 2x - 10

Next, add 4 to both sides

• y = 2x - 6

Now, we have the equation for the line in slope-intercept form. Both of the equations technically meet the requirements for the question, but slope-intercept is more common to use.