Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither.
3x - 4y = -3
8x + 6y = -3
slope of 3x - 4y = -3 is 3/4
slope of 8x + 6y = -3 is -8/6 = -4/3
what have you learned about the slopes of perpendicular lines ?
To determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither, we need to compare their slopes. The standard form of a linear equation is given by the equation: Ax + By = C.
To find the slope of a line from its equation in the standard form, we need to rearrange the equation and solve for y, getting the equation into slope-intercept form, y = mx + b, where m represents the slope.
Let's find the slopes of the two given equations:
1) 3x - 4y = -3:
To get the equation in slope-intercept form, solve for y:
-4y = -3x - 3
Divide by -4:
y = (3/4)x + (3/4)
2) 8x + 6y = -3:
Again, solve for y:
6y = -8x - 3
Divide by 6:
y = (-8/6)x - (3/6)
Simplify:
y = (-4/3)x - (1/2)
Now that we have both equations in slope-intercept form, we can determine their slopes.
For the first equation, y = (3/4)x + (3/4), the slope is 3/4.
For the second equation, y = (-4/3)x - (1/2), the slope is -4/3.
Since the slopes are not equal and not negative reciprocals of each other, these lines are neither parallel nor perpendicular.