How to write the slope intercept form of the equation of the line described; (-2,-1) parallel to y=-3/2x-1?

Question

30688 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-29T21:05:57

See a solution process below:

The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

#y = color(red)(-3/2)x - color(blue)(1)#

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

Therefore the slope of this line is: #color(red)(m = -3/2)#

Parallel lines by definition have the same slope. Therefore, we can substitute this slope into the formula giving:

#y = color(red)(-3/2)x + color(blue)(b)#

We have been given a point on the parallel line so we can substitute the values of the point for #x# and #y# and solve for #color(blue)(b)#

#y = color(red)(-3/2)x + color(blue)(b)# becomes:

#-1 = (color(red)(-3/2) xx -2) + color(blue)(b)#

#-1 = color(red)(3) + color(blue)(b)#

#-3 - 1 = -3 + color(red)(3) + color(blue)(b)#

#-4 = 0 + color(blue)(b)#

#-4 = color(blue)(b)#

We can now substitute the slope and y-intercept into the formula giving:

#y = color(red)(-3/2)x + color(blue)(-4)#

#y = color(red)(-3/2)x - color(blue)(4)#