Question

write an equation in point - slope form of the line that passes through the given points, then write the equation in slope - intercept form. (-3,5), (9,1)
what is the point - slope form of the equation of the line?
(simplify your answer. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $(x_1,y_1)=(-3,5)$ and $(x_2,y_2)=(9,1)$, then $m=\frac{1 - 5}{9-(-3)}=\frac{-4}{12}=-\frac{1}{3}$.

Step2: Write the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(-3,5)$ and $m =-\frac{1}{3}$, we get $y - 5=-\frac{1}{3}(x+3)$.

Step3: Convert to slope - intercept form

Start with $y - 5=-\frac{1}{3}(x + 3)$. Distribute on the right side: $y-5=-\frac{1}{3}x - 1$. Add 5 to both sides: $y=-\frac{1}{3}x+4$.

Answer:

Point - slope form: $y - 5=-\frac{1}{3}(x + 3)$
Slope - intercept form: $y=-\frac{1}{3}x + 4$