Question

What is the equation of the line described below written in slope-intercept form? The line passing through point (0,0) and parallel to the line whose equation is 3x+2y-6=0

Answer 1

Answer:

$y = - \frac{ 3}{2} x$

Step-by-step explanation:

slope-intercept form

y= mx +c, where m is the slope and c is the y-intercept.

Let's rewrite the given equation into the slope-intercept form so we can find out its gradient.

3x +2y -6= 0

2y= -3x +6

Dividing by 2 throughout:

$y = - \frac{3}{2} x + 3$

Thus gradient of given line= $- \frac{3}{2}$

Parallel lines have the same gradient.

Thus gradient of line= $- \frac{3}{2}$

Subst. m=$- \frac{3}{2}$ into the equation:

$y = - \frac{3}{2}x + c$

To find c, substitute a pair of coordinates.

When x=0, y=0,

$0 = - \frac{3}{2} (0) + c \\ c = 0$

Thus, the equation of the line is $y = - \frac{3}{2} x$.