a line has a slope of 2 and passes through the point (2, 14). write its equation in slope - intercept form…

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.

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.

Answer

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. Given $m = 2$, the equation becomes $y=2x + b$.

Step2: Substitute the point values

Substitute $x = 2$ and $y = 14$ into $y = 2x + b$. So, $14=2\times2 + b$.

Step3: Solve for $b$

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

Step4: Write the final equation

Substitute $b = 10$ back into $y = 2x + b$. The equation of the line is $y=2x + 10$.

Answer:

$y = 2x+10$