Question

write the slope-intercept form of the equation of the line passing through the point (5, -4) and perpendicular to the line y= - 4/3 x + 5

Answer 1

The slope-intercept form of the equation for a line perpendicular to y = -4/3x + 5 and passing through the point (5, -4) is y = (3/4)x - 19/4.

Step-by-step explanation:

To find the equation of a line perpendicular to a given line, we need to determine its slope first. The given line has a slope of -4/3. Perpendicular lines have negative reciprocal slopes, so the slope of the line we are looking for will be 3/4. Now, we can use the point-slope form of a line, where the slope is m and the given point is (x1, y1):

y - y1 = m(x - x1)

Substituting the values from the given point (5, -4) and the slope 3/4, we get:

y - (-4) = (3/4)(x - 5)

Expanding and rearranging the equation, we get the slope-intercept form:

y = (3/4)x - 19/4