Question

Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible.

Answer 1

Answer:

y=-x+18

Step-by-step explanation:

Equation of a line

A line can be completely defined by two points. Suppose we know the line passes through points A(x1,y1) and B(x2,y2).

The equation for a line can be written as:

$y=mx+b$

Where m is the slope and b is the y-intercept. Both values can be determined by using the coordinates of the given points.

First, determine the slope with the equation:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

The points are: A(15,3) B(3,15)

$\displaystyle m=\frac{15-3}{3-15}=\frac{12}{-12}=-1$

The equation of the line can be written as:

$y=-x+b$

Now, use any point to determine the value of b. Substitute (15,3):

$3=-15+b$

Solve for b:

b=18

The equation of the line is

y=-x+18

The slope is -1 and the y-intercept is 18.