Question

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

Answer 1

Answer:

a = -6/5

Step-by-step 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

$5y=-2x+10\\\\y=\frac{-2x+10}{5} \\\\y=\frac{-2}{5}x+\frac{10}{5} \\\\y=\frac{-2}{5}x+2$

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

$3y=ax-15\\\\y=\frac{ax-15}{3} \\\\y=\frac{ax}{3}-\frac{15}{3} \\\\y=\frac{a}{3}x-5$

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,

$m_1=m_2\\\\\frac{-2}{5}=\frac{a}{3}\\\\-2(3)=a(5)\\\\-6=5a\\-6/5=a$

so the value of a equals

a= -6/5