Question 1186763

The line containing a slope of {{{3}}} and a y-intercept of {{{-2}}}.



given:
{{{m=3}}}

y-intercept of {{{-2}}}

use slope intercept form:

{{{y=mx+b}}} where  {{{m}}} is a slope and {{{b}}} is y-intercept

substitute given values

{{{y=3x-2}}}


Write the standard form of the line that passes through the point ({{{1}}},{{{5}}}) and is parallel to the x-axis. Include your work in your final answer. Type your answer in the box provided to submit your solution.

answer:

the line that passes through the point ({{{1}}},{{{5}}}) and is parallel to the x-axis is horizontal line {{{y=5}}} 



Write the standard form of the line that contains a slope of {{{-1/2}}} and y-intercept of {{{1}}}. Include your work in your final answer. Type your answer in the box provided to submit your solution.

first use slope intercept form

{{{y=mx+b}}} where  {{{m=-1/2}}} is a slope and {{{b=1}}} 

{{{y=-(1/2)x+1}}}  ....both sides multiply by {{{2}}}

{{{2y=-x+2}}}

{{{x+2y=2}}}->the standard form of the line



Write the standard form of the line that contains a y-intercept of{{{ -3}}} and passes through the point ({{{3}}},{{{0}}}) . Include your work in your final answer. Type your answer in the box provide to submit your solution.

use point slope formula:

{{{y-y[1]=m(x-x[1])}}} 

given:   

({{{x[1]}}},{{{y[1]}}}) =({{{3}}},{{{0}}}) 

{{{b=-3}}}->  ({{{x[2]}}},{{{y[2]}}}) =({{{0}}},{{{-3}}}) 

find a slope: {{{m=(y[2]-y[1])/(x[2]-x[1])=(-3-0)/(0-3)=-3/-3=1}}}

{{{y-0=1(x-3)}}} 

{{{y=x-3}}} 

{{{-x+y=-3}}} ->the standard form of the line