what is an equation of the line that passes through the points (3,1) and (-3, -7)
Mathematics · Middle School · Mon Jan 18 2021
Answered on
Given the points:
(3, 1)
(-3, 7)
x1= 3
x2 = -3
y1 = 1
y2= 7
Write the equation of the line.
The equation of the line can be written in point-slope form, and then slope-intercept form
Point-slope form:
y - y1 =m(x -x1)
Slope-intercept form:
y = mx + b
Solution:
Before we can write in point-slope form, we must first find the slope of the line, we can find the slope by using the slope formula.
m = y2 -y1 /x2 -x1
m= (7 -1)/(-3 - 3)
m = 6/-6
m= -1
Substitute the given values of x1, m and y1 to the formula for the point-slope form.
y - 1 = 1( x -3)
Point-slope form : y - 1 = x - 3
In order to change to slope-intercept form, we simply need to transpose -1 on the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.
y = x - 3 + 1
Slope-intercept form: y = x - 2
Final answer:
Point-slope form : y - 1 = x - 3
Slope-intercept form: y = x - 2