a line has a slope of $\frac{5}{7}$ and passes through the point (12, 9). write its equation in slope…

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 $m=\frac{5}{7}$, so the equation is $y=\frac{5}{7}x + b$.

Step2: Substitute the point values

Substitute $x = 12$ and $y = 9$ into the equation $y=\frac{5}{7}x + b$. We get $9=\frac{5}{7}\times12 + b$.

Step3: Solve for $b$

First, calculate $\frac{5}{7}\times12=\frac{60}{7}$. Then the equation becomes $9=\frac{60}{7}+b$. Rewrite 9 as $\frac{63}{7}$, so $\frac{63}{7}=\frac{60}{7}+b$. Subtract $\frac{60}{7}$ from both sides: $b=\frac{63}{7}-\frac{60}{7}=\frac{3}{7}$.

Step4: Write the final equation

Substitute $b = \frac{3}{7}$ back into $y=\frac{5}{7}x + b$. The equation of the line is $y=\frac{5}{7}x+\frac{3}{7}$.

Answer:

$y=\frac{5}{7}x+\frac{3}{7}$