Question

For what value of “a”are the graphs of 5y = -2x + 10 and 3y = aX- 15 parallel

Answer 1

a = -6/5

Explanation:

For the graphs to be parallel the graphs should have same slope(m)

So we rewrite both our equations in the slope-intercept form then compare the slope to find the value of a like this,

`y=mx+b`

This equation is the slope-intercept form we convert both our equations in this form firstly taking equation 1

`5y=-2x+10\\\\y=(-2x+10)/(5) \\\\y=(-2)/(5)x+(10)/(5) \\\\y=(-2)/(5)x+2`

so if we compare it with y = mx + b the coefficient of x is m and hence

m= -2/5 now solving for equation 2

`3y=ax-15\\\\y=(ax-15)/(3) \\\\y=(ax)/(3)-(15)/(3) \\\\y=(a)/(3)x-5\\\\`

so here if we compare it with y = mx + b the coeffienct of x is a/3 so since parallel lines have same slope by the formula:

`m_1=m_2`

we equation both the slope to each other to find the value of a like this,

`m_1=m_2\\\\(-2)/(5)=(a)/(3)\\\\-2(3)=a(5)\\\\-6=5a\\-6/5=a`

so the value of a equals

a= -6/5