Answer:
parallel
Step-by-step explanation:
Let's rewrite each equation into the slope-intercept form so that we can easily identify the slope of each line.
slope-intercept form: y= mx +c, where m is the gradient and c is the y-intercept.
9x +3y= 12
3x +y= 4 (÷3 throughout)
y= -3x +4 -----(1)
24x +8y= 35
8y= -24x +35 (-24x on both sides)
[tex]y = - 3x+ 4 \frac{3}{8} [/tex] -----(2)
Thus, the slopes of the lines are both -3. Since both lines have the same gradient, they are parallel to each other.
Notes:
• parallel lines have the same gradient
• the product of the gradients of two perpendicular lines is -1
• gradient and slope has the same meaning and can thus be used interchangeably
