154k views
3 votes
Write the equation, in slope-intercept form, of the line that passes through (-2,0) and is parallel to the line represented by 5x-3y=-17 .

User Electra
by
8.3k points

1 Answer

5 votes

Answer:


y=(5)/(3)x+(10)/(3)

Explanation:

Firstly we rewrite the equation that is parallel to the line we need because parallel lines have the same slope by the rule


m_1=m_2

so we rewrite the equation in slope-intercept form:


5x-3y=17\\-3y=-5x+17\\y=(-5x+17)/(-3)\\\\y=(-5x)/(-3)+(17)/(-3) \\\\y=(5)/(3)x-(17)/(3)

and now we compare it with our slope-intercept form equation:


y=mx+b

the coefficient of x which is m is the slope and since parallel lines have equal slopes the line that we need would also have the same slope which is 5/3.

now the next step is the line that we need passes through the point (-2,0) so it means that it should satisfy that specific point so we insert that point into our slope-intercept form and insert the slope which is 5/3 which is m.


y=mx+b\\y=(5)/(3)x+b\\\\0=(5)/(3)(-2)+b\\\\0=(-10)/(3)+b\\\\b=(10)/(3)\\

now we know that the y-intercept(b) of the line we need is 10/3 and slope(m) is 5/3 insert these values into our slope-intercept form:


y=mx+b\\y=(5)/(3)x+(10)/(3) \\

so this is our given line.

User DarkerIvy
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.