Unit what is the equation of a line that is perpendicular to -3x + 4y = 4 and passes through the point (4,0)

ANSWER

Or

EXPLANATION

Let us find the gradient of the line:

by rewriting it in the slope intercept form.

We divide through by 4 now;

This is now in the form;

where

is he slope.

This implies that the slope of the line that is perpendicular to this line will be the negative reciprocal of .

Thus the perpendicular line has slope,

.

Let the perpendicular line have equation,

When we substitute the slope we have;

We substitute the point. to find c.

We substitute c to obtain;

Or

y = -4/3x + 16/3 or 4x + 3y = 16

Step-by-step explanation:

We know that the standard form of equation for a line is:

where is the slope of the line and is the y-intercept.

So writing the given equation in the standard form:

According to this equation, the slops (m) is 3/4. So the slope of line perpendicular to this would be negative reciprocal of 3 i.e. -4/3.

Putting the value of the slope and the given point to find the y-intercept:

Therefore, the equation of line perpendicular to -3x + 4y = 4 which passes through the point (4,0) is or 4x + 3y = 16.

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step-by-step explanation: