25.0k views
3 votes
Slope and y intercept of a line that passes through the points (-3,1) and (7,-5)?

1 Answer

3 votes

Answer:

The slope of the line is -3/5

The y-intercept of the line is 14/5

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 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:


\displaystyle m=(y_2-y_1)/(x_2-x_1)

The points are: A(-3,1) B(7,-5)


\displaystyle m=(-5-1)/(7-(-3))


\displaystyle m=(-6)/(7+3)=(-6)/(10)

Simplifying by 2:


\displaystyle m=-(3)/(5)

The slope of the line is -3/5

Using this value in the equation of the line:


\displaystyle y=-(3)/(5)x+b

Use any of the given points to find b. Susbstituting point A(-3,1):


\displaystyle 1=-(3)/(5)(-3)+b

Operating:


\displaystyle 1=-(9)/(5)+b

Moving the constants to the left side:


\displaystyle 1+(9)/(5)=b\Rightarrow b=(14)/(5)


\boxed{\displaystyle b=(14)/(5)}

The y-intercept of the line is 14/5

User Sherian
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories