How do you write an equation of a line given (-2,0) and (0,6)?

2 Answers
May 30, 2017

See a solution process below:

Explanation:

First, we need to determine the slope of the line. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.

Substituting the values from the points in the problem gives:

#m = (color(red)(6) - color(blue)(0))/(color(red)(0) - color(blue)(-2)) = (color(red)(6) - color(blue)(0))/(color(red)(0) + color(blue)(2)) = 6/2 = 3#

The point #(0, 6)# is also the #y# intercept. Therefore we can use the slope-intercept formula to find an equation for the line. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

Substituting the slope we calculated and the y-intercept gives:

#y = color(red)(3)x + color(blue)(6)#

May 30, 2017

#y=3x+6#

Explanation:

First let's find the slope, #m#:

#m=frac(y_2-y_1)(x_2-x_1)#

#m=frac(6-0)(0-(-2))#

#m=frac(6)(2)=3#

Now, let's use the point slope formula of a line:

#y-y_1=m(x-x_1)#

and plug in #m=3# and one of the given points:

#y-0=3(x-(-2))#

#y=3x+6#