Write an equation in slope-intercepts form for the line that passes through (5, -4) and is perpendicular to the line described by 2x-10y=0 EXPLAIN what you did in each step to arrive at your answer plz

y = -5x + 21

Step-by-step explanation:

First, put 2x - 10y = 0 into slope intercept form to find the slope:

Subtract 2x from both sides:

-10y = -2x

Divide each side by -10:

-10y = -2x

y = 1/5x

So, the slope of the line is 1/5.

Perpendicular lines have opposite reciprocal slopes, so the slope of the other line will be -5.

Then, use the equation y = mx + b to plug in the slope and the point given.

Solve for b:

y = mx + b

-4 = -5(5) + b

-4 = -25 + b

21 = b

Lastly, plug in the slope and b into y = mx + b to create the equation in slope intercept form:

y = -5x + 21 is the equation