Question

a line has a slope of -1 and passes through the point (-14, 15). 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 and point - slope form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. We know that $m=- 1$ and the point $(x_1,y_1)=(-14,15)$.

Step2: Substitute into point - slope form

Substitute $m = - 1$, $x_1=-14$ and $y_1 = 15$ into the point - slope form:
$y-15=-1(x - (-14))$
Simplify the right - hand side: $y - 15=-1(x + 14)$

Step3: Distribute the slope

Using the distributive property $a(b + c)=ab+ac$, we have:
$y-15=-x-14$

Step4: Solve for y (get into slope - intercept form)

Add 15 to both sides of the equation:
$y=-x-14 + 15$
Simplify the right - hand side: $y=-x + 1$

Answer:

$y=-x + 1$