Question

Huuuurrry plllzzzzzz. Determine the equation of the line that passes through the given points (2,6) and (4,16)

Answer 1

Linear Equations

Linear equations are typically organized in slope-intercept form:

`y=mx+b`

• m is the slope of the line
• b is the y-intercept (the value of y when the line passes through the y-axis)

To find linear equations in slope-intercept form:

1. Determine the slope
2. Plug the slope into the general form
3. Determine the y-intercept by isolating b
4. Plug the b back into the equation

Solving the Question

We're given:

• The line passes through the points (2,6) and (4,16)

First, determine the slope of the line.

`m=(y_2-y_1)/(x_2-x_1)` where
`(x_1,y_1)` and
`(x_2,y_2)` are points that fall on the line

⇒ Plug in the given points (2,6) and (4,16):

`m=(16-6)/(4-2)\\\\m=(10)/(2)\\\\m=5`

⇒ Therefore, the slope of the line is 5. Plug this back into the general form:

`y=5x+b`

Now, determine the y-intercept.

`y=5x+b`

⇒ Plug in one of the given points:

`6=5(2)+b\\6=10+b\\b=-4`

⇒ Therefore, the y-intercept is -4. Plug this back into our original equation:

`y=5x-4`

Answer

`y=5x-4`