Question

a line has a slope of $\frac{5}{6}$ and passes through the point (7, 6). 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. Given $m=\frac{5}{6}$, the equation becomes $y=\frac{5}{6}x + b$.

Step2: Substitute the point values

Substitute $x = 7$ and $y = 6$ into $y=\frac{5}{6}x + b$. So, $6=\frac{5}{6}\times7 + b$.

Step3: Solve for $b$

First, calculate $\frac{5}{6}\times7=\frac{35}{6}$. Then the equation is $6=\frac{35}{6}+b$. Rewrite 6 as $\frac{36}{6}$. So, $\frac{36}{6}=\frac{35}{6}+b$. Subtract $\frac{35}{6}$ from both sides: $b=\frac{36}{6}-\frac{35}{6}=\frac{1}{6}$.

Step4: Write the final equation

Substitute $b = \frac{1}{6}$ back into $y=\frac{5}{6}x + b$. The equation of the line is $y=\frac{5}{6}x+\frac{1}{6}$.

Answer:

$y=\frac{5}{6}x+\frac{1}{6}$