What is an equation of the line that passes through the point left bracket, 4, comma, 0, right bracket(4,0) and is perpendicular to the line 4, x, minus, 3, y, equals, 154x−3y=15?

Sure, let's solve this step by step.

Step 1: Find the slope of the given line The equation of the given line is 4x - 3y = 15. We can rewrite this in the slope-intercept form (y = mx + b) to find the slope (m).

4x - 3y = 15 => 3y = 4x - 15 => y = (4/3)x - 5

So, the slope of the given line is 4/3.

Step 2: Find the slope of the line perpendicular to the given line The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. So, the slope of the line we're looking for is -1/(4/3) = -3/4.

Step 3: Use the point-slope form to find the equation of the line The point-slope form of the equation of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We know that our line passes through the point (4, 0), so we can substitute m = -3/4, x1 = 4, and y1 = 0 into the point-slope form:

y - 0 = -3/4(x - 4) => y = -3/4x + 3

So, the equation of the line that passes through the point (4, 0) and is perpendicular to the line 4x - 3y = 15 is y = -3/4x + 3.