Tell whether the lines for each pair of equations are parallel, perpendicular, or neither. y = –4x + 3 –2x + 8y = 5 (1 point) Responses parallel perpendicular neither
To determine whether the lines given by the pair of equations are parallel, perpendicular, or neither, we need to examine their slopes.
The given equations are:
y = -4x + 3 ...(1)
-2x + 8y = 5 ...(2)
To find the slope of equation (1), we can rewrite it in the form y = mx + b, where m represents the slope:
y = -4x + 3
Comparing this to the standard form, y = mx + b, we can see that the slope of equation (1) is -4.
To find the slope of equation (2), we can rewrite it in slope-intercept form:
-2x + 8y = 5
8y = 2x + 5
Dividing both sides by 8:
y = (2/8)x + 5/8
Simplifying:
y = (1/4)x + 5/8
Comparing this to the standard form, y = mx + b, we can see that the slope of equation (2) is 1/4.
Now that we have the slopes, we can determine the relationship between the lines. If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals of each other (when multiplied, the result is -1), the lines are perpendicular. If neither condition is met, the lines are neither parallel nor perpendicular.
The slope of equation (1) is -4, and the slope of equation (2) is 1/4. Since these slopes are not equal and not negative reciprocals of each other, we can conclude that the lines given by the pair of equations are neither parallel nor perpendicular.
Therefore, the correct response is: neither.