Answer:
The slope of the line is -3/5
The y-intercept of the line is 14/5
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 m 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(-3,1) B(7,-5)
[tex]\displaystyle m=\frac{-5-1}{7-(-3)}[/tex]
[tex]\displaystyle m=\frac{-6}{7+3}=\frac{-6}{10}[/tex]
Simplifying by 2:
[tex]\displaystyle m=-\frac{3}{5}[/tex]
The slope of the line is -3/5
Using this value in the equation of the line:
[tex]\displaystyle y=-\frac{3}{5}x+b[/tex]
Use any of the given points to find b. Susbstituting point A(-3,1):
[tex]\displaystyle 1=-\frac{3}{5}(-3)+b[/tex]
Operating:
[tex]\displaystyle 1=-\frac{9}{5}+b[/tex]
Moving the constants to the left side:
[tex]\displaystyle 1+\frac{9}{5}=b\Rightarrow b=\frac{14}{5}[/tex]
[tex]\boxed{\displaystyle b=\frac{14}{5}}[/tex]
The y-intercept of the line is 14/5
