What is the slope-intercept form of the line passing through # (0, 6) # and # (3,0) #?

2 Answers
Jun 8, 2018

Answer:

# y = -2x + 6 #

Explanation:

In the slope intercept form # y = mx + b#
m = the slope ( think mountain ski slope. )
b = the y intercept ( think beginning )

The slope can be found by #( y_1 - y_2)/(x_1 - x_2)#

putting the values for the points into the equation gives

# (6-0)/(0-3)# = # 6/-3#= #-2 #

Putting this value for m the slope into an equation with one set of value for a point can be used to solve for b

# 6 = -2(0) + b #

This gives

# 6 = b#

so

# y = -2x + 6#

Answer:

#color(red)(y) = -2color(green)(x) + 6#

Explanation:

First of all, You have to use the #color(Brown)("Point-Slope Form")# of Linear Equations to get the Slope of the line.

The Point-Slope Form of a Linear Equation is:-

#color(blue)(m) = color(Red)(y_2 - y_1)/color(Green)(x_2-x_1)#

Where #(color(green)(x_1), color(red)(y_1))# and #(color(green)(x_2), color(red)(y_2))# are the points on the line.

So, The Slope for the Required Line

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

Now, We can use the Slope - Intercept Form.

So, The Equation becomes,

#color(white)(xxx)color(red)(y) = color(blue)(m)color(green)(x) + color(SkyBlue)(c)#

#rArr color(red)(y) = -2color(green)(x) + color(SkyBlue)(c)#.

We have been told that The Line has a Point #(3,0)# on it.

So, The Co-ordinates of that Point must satisfy the Equation.

So,

#color(white)(xxx)0 = -2 xx 3 + color(skyblue)(c)#

#rArr color(skyblue)(c) - 6 = 0#

#rArr color(skyblue)(c) = 6#

So, The Final Equation is,

#color(red)(y) = -2color(green)(x) + 6#.

Hope this helps, and I really hope that my colour choice isn't too much bad.