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 becomes $y=2x + b$.

Step2: Substitute the point into the equation

We know the line passes through the point $(2,14)$. Substitute $x = 2$ and $y = 14$ into the equation $y=2x + b$:
$$14=2\times2 + b$$
$$14 = 4 + b$$

Step3: Solve for b

Subtract 4 from both sides of the equation $14 = 4 + b$:
$$b=14 - 4$$
$$b = 10$$

Step4: Write the final equation

Now that we know $m = 2$ and $b = 10$, substitute these values into the slope - intercept form $y=mx + b$:
$$y=2x+10$$

Answer:

$y = 2x+10$