Determine if the graphs of the equations are parallel, perpendicular, or neither:
4x – 3y = 6
8x – 6y = 9
slope of first = 4/3
slope of 2nd = 8/6 = 4/3
notice that x1/x2 = y1/y2 ≠ c1/c2
so they are two parallel lines
To determine if the graphs of the equations are parallel, perpendicular, or neither, we need to compare their slopes. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
Let's rearrange the given equations in slope-intercept form:
Equation 1: 4x - 3y = 6
Rearranging, we get: 4x - 6 = 3y
Dividing by 3, we get: (4/3)x - 2 = y
So, the slope of equation 1 is 4/3.
Equation 2: 8x - 6y = 9
Rearranging, we get: 8x - 9 = 6y
Dividing by 6, we get: (8/6)x - 3/2 = y
Reducing, we get: (4/3)x - 3/2 = y
So, the slope of equation 2 is also 4/3.
Since both equations have the same slope, which is 4/3, the graphs of the equations are parallel.