Question #59258

2 Answers
Mar 14, 2017

Answer:

See the entire solution explanation below.

Explanation:

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)#

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

For this problem:

#y = color(red)(10)x + color(blue)(100)#

Therefore:

The slope is: #color(red)(m) = 10#

The y-intercept is: #color(blue)(b = 100)# or #(0, 100)#

To find the x-intercept, set #y# equal to #0# and solve for #x#:

#0 = color(red)(10)x + color(blue)(100)#

#0 - 100 = color(red)(10)x + color(blue)(100) = 100#

#-100 = color(red)(10)x + 0#

#-100 = color(red)(10)x#

#-100/10 = (color(red)(10)x)/10#

#-10 = (cancel(color(red)(10))x)/color(red)(cancel(color(black)(10)))#

#-10 = x#

#x = -10#

Therefore:

The x-intercept is: #x = -10# or #(-10, 0)#

Mar 14, 2017

Answer:

y-int = (0, 100)
slope = 10
x-int = (-10, 0)

Explanation:

To find the Y-intercept of a line when it is written in Y-intercept form like it is above, you look at the number without the variable, if you want a technical answer you find it by setting #x=0# and solving for y which would give you 100 in either case.

The slope is found by looking at the coefficient of the x term which in this case is 10.

To find the X-intercept, do the opposite of what you did to find the Y-intercept and set y equal to 0 and solve for x like follows:

#0 = 10x + 100#

Get the terms with x alone on one side and the terms without x on the other side as such

#-100 = 10x#

And get x by itself by dividing both sides by 10 to get the answer

#-10 = x#