Question

Write an equation in slope-intercept form of the line that passes through the points (2, 4) and (3,6).

Answer 1

Answer:

$y=2x$

Step-by-step explanation:

We want to write an equation in slope-intercept form that passes through the points (2, 4) and (3, 6).

So, we will first find the slope. Let (2, 4) be (x₁, y₁) an let (3, 6) be (x₂, y₂).

The slope formula is given by:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

So, by substitution, our slope is:

$\displaystyle m=\frac{6-4}{3-2}=\frac{2}{1}=2$

Now, we can use the point-slope form:

$y-y_1=m(x-x_1)$

By substitution:

$y-(4)=2(x-(2))$

Distribute:

$y-4=2x-4$

Adding 4 to both sides yields:

$y=2x$

And we have our equation.

In this case, the y-intercept is 0.