Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither.
12x + 4y = 16
5y - 22 = -15x
put the in slope intercept form:
y= -3x+4
y=-3x+22/5
same slope, parallel
To determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither, we need to compare their slopes.
First, let's rewrite both equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Equation 1: 12x + 4y = 16
To write this equation in slope-intercept form, we isolate y:
4y = -12x + 16
y = (-12/4)x + 4
y = -3x + 4
Equation 2: 5y - 22 = -15x
To write this equation in slope-intercept form, we isolate y:
5y = -15x + 22
y = (-15/5)x + (22/5)
y = -3x + (22/5)
Now that we have both equations in slope-intercept form, we can compare their slopes. Since the coefficient of x in both equations is -3, we can see that both equations have the same slope.
Therefore, the graphs of the equations are parallel lines since they have the same slope (-3).
To determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither, we need to compare their slopes.
Let's rewrite the given equations in the slope-intercept form, y = mx + b, where m represents the slope:
Equation 1: 12x + 4y = 16
First, isolate y:
4y = -12x + 16
Divide both sides by 4:
y = -3x + 4
Equation 2: 5y - 22 = -15x
First, isolate y:
5y = -15x + 22
Divide both sides by 5:
y = -3x + 4.4
Comparing the two equations, we can see that both equations have the same slope, which is -3.
Since the slopes are the same, the graphs of the equations are parallel lines.