Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = –one-fourthx + 10
–2x + 8y = 6
To determine whether the lines are parallel, perpendicular, or neither, we need to compare the slopes of the two lines.
Equation 1: y = -1/4x + 10
The slope of this line is -1/4. Since the equation is in slope-intercept form (y = mx + b), where m is the slope, the coefficient of x (-1/4) represents the slope.
Equation 2: -2x + 8y = 6
Let's manipulate this equation to solve for y in terms of x, so it is in the slope-intercept form.
-2x + 8y = 6
8y = 2x + 6
y = 1/4x + 3/4
The slope of this line is 1/4.
Now, let's compare the slopes:
Slope of Equation 1: -1/4
Slope of Equation 2: 1/4
Since the slopes are negative reciprocals of each other, the lines are perpendicular.