Question

a line passes through the point (4, 9) and has a slope of -\frac{3}{2}. write an equation in slope - intercept form for this line.

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 $m=-\frac{3}{2}$, so the equation becomes $y =-\frac{3}{2}x + b$.

Step2: Substitute the point into the equation

Substitute the point $(x = 4,y = 9)$ into the equation $y=-\frac{3}{2}x + b$. We get $9=-\frac{3}{2}\times4 + b$.

Step3: Solve for $b$

First, calculate $-\frac{3}{2}\times4=-6$. Then the equation $9=-6 + b$ can be solved for $b$ by adding 6 to both sides. So $b=9 + 6=15$.

Step4: Write the final equation

Substitute $b = 15$ back into $y=-\frac{3}{2}x + b$. The equation of the line in slope - intercept form is $y=-\frac{3}{2}x+15$.

Answer:

$y =-\frac{3}{2}x + 15$