Question

The equation of line m is 4x - 5y = -2. What is the slope of a line that is perpendicular to line m?

Answer 1

To find the slope of a line perpendicular to line m with equation 4x - 5y = -2, we convert the equation into slope-intercept form yielding a slope of 4/5. Therefore, the slope of the perpendicular line is the negative reciprocal, which is -5/4.

Step-by-step explanation:

To find the slope of a line that is perpendicular to line m, which has the equation 4x - 5y = -2, we first need to put this equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Solving for y, we get y = (4/5)x + 2/5, indicating that the slope of line m is 4/5. Since the slope of any line perpendicular to this would be the negative reciprocal of 4/5, the slope of the line perpendicular to m is -5/4.

Knowing the slope-intercept equation and understanding that perpendicular lines have slopes that are negative reciprocals of each other helps us solve this problem. When the equation of a line is given in standard form (Ax + By = C), converting it to slope-intercept form allows us to easily identify the slope, and consequently, determine the slope for any perpendicular line.

Answer 2

The slope of a line perpendicular to line m is 4/5.

Step-by-step explanation:

In order to find the slope of a line perpendicular to line m, we need to consider the fact that the product of the slopes of two perpendicular lines is always -1. The given equation of line m is in the form Ax - By = C, where A is the coefficient of x, B is the coefficient of y, and C is the constant term. In this case, the coefficient of x is 4, and the coefficient of y is -5.

The slope of line m can be found by rearranging the equation into the slope-intercept form (y = mx + b), where m is the slope. By isolating y, we get y = (4/5)x + (2/5). The slope of line m is 4/5.

Now, to find the slope of a line perpendicular to m, we take the negative reciprocal of the slope of m. The negative reciprocal of 4/5 is -5/4. Therefore, the slope of a line perpendicular to line m is -5/4. This means that if you have a line with a slope of 4/5, a line perpendicular to it will have a slope of -5/4.