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.

$m=\dfrac{y_2-y_1}{x_2-x_1}$ 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):

$m=\dfrac{16-6}{4-2}\\\\m=\dfrac{10}{2}\\\\m=5$

⇒ 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

$y=5x-4$