Question

write the point - slope form of the lines equation satisfying the given conditions. then use the point - slope form of the equation to write the slope - intercept form of the equation in function notation
passing through (-8,26) and (-4,14)

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.)
let f be the name of the function. what is the slope - intercept form of the equation of the line in function notation?
(simplify your answer. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1, y_1)=(-8, 26)\) and \((x_2, y_2)=(-4, 14)\). So, \( m=\frac{14 - 26}{-4-(-8)}=\frac{-12}{4}=-3 \).

Step2: Write the point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((-8, 26)\) and \( m = - 3 \), we get \( y - 26=-3(x + 8) \) (we can also use the other point \((-4,14)\), for example, using \((-4,14)\) we would have \( y - 14=-3(x + 4) \), both are correct).

Step3: Convert to slope - intercept form

Start with \( y - 26=-3(x + 8) \). Expand the right - hand side: \( y - 26=-3x-24 \). Then add 26 to both sides: \( y=-3x - 24 + 26=-3x+2 \). In function notation, \( f(x)=-3x + 2 \).

Answer:

The point - slope form of the equation of the line is \( y - 26=-3(x + 8) \) (or \( y - 14=-3(x + 4) \)).
The slope - intercept form of the equation of the line in function notation is \( f(x)=-3x + 2 \).