Question

a line has a slope of 2 and passes through the point (2, 14). write its equation in slope-intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that $m = 2$. So the equation of the line is $y=2x + b$.

Step2: Substitute the point into the equation

We know that the line passes through the point $(2,14)$. Substitute $x = 2$ and $y = 14$ into the equation $y=2x + b$:
$$14=2\times2 + b$$

Step3: Solve for $b$

First, calculate $2\times2=4$. Then the equation becomes $14 = 4 + b$. Subtract 4 from both sides of the equation: $b=14 - 4=10$.

Step4: Write the final equation

Now that we know $m = 2$ and $b = 10$, the equation of the line in slope - intercept form is $y = 2x+10$.

Answer:

$y = 2x + 10$