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

Question

Hazel Anglin · Accepted Answer

#y=3x+6#

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#

Abigail Allen · Answer

See a solution process below:

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)#

Abigail Allen · Answer

undefined To write an equation of a line given two points, first find the slope using the formula (y2 - y1) / (x2 - x1). Once you have the slope, use one of the points and the slope in the point-slope form of the equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the points.