Question

Write the equation of the line perpendicular to y = 4/5x + 7/5 that passes through the point (-9, 4). Type in the equation using slope-intercept form or using the given point and point-slope form.

Answer 1

To find the equation of the line perpendicular to y = 4/5x + 7/5 that passes through the point (-9, 4), we need to determine the slope of the given line and use the point-slope form. The equation of the perpendicular line is y = -5/4x + 29/4.

Step-by-step explanation:

To find the equation of the line perpendicular to y = 4/5x + 7/5 that passes through the point (-9, 4), we first need to determine the slope of the given line. The given line is in slope-intercept form, y = mx + b, where m represents the slope. In this case, the slope of the given line is 4/5. The slope of a line perpendicular to another line is the negative reciprocal of the slope of that line. So, the slope of the perpendicular line is -5/4.

Now that we have the slope of the perpendicular line, we can use the point-slope form of a linear equation: y - y1 = m(x - x1). Substituting the values -9 for x1, 4 for y1, and -5/4 for m gives us the equation y - 4 = -5/4(x - (-9)).

Simplifying this equation further gives us the equation of the line perpendicular to y = 4/5x + 7/5 that passes through the point (-9, 4) as y = -5/4x + 29/4.