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:
[tex]y=mx+b[/tex]
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:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The points are: A(15,3) B(3,15)
[tex]\displaystyle m=\frac{15-3}{3-15}=\frac{12}{-12}=-1[/tex]
The equation of the line can be written as:
[tex]y=-x+b[/tex]
Now, use any point to determine the value of b. Substitute (15,3):
[tex]3=-15+b[/tex]
Solve for b:
b=18
The equation of the line is
y=-x+18
The slope is -1 and the y-intercept is 18.
