write an equation of a line containing the given point and perpendicular to the given line(4,7);4x+y=8
To find the equation of a line perpendicular to the given line, we need to determine the slope of the given line, and then calculate the negative reciprocal of that slope.
First, let's rewrite the given equation in slope-intercept form (y = mx + b) by isolating y:
4x + y = 8
y = -4x + 8
We can see that the slope of the given line is -4.
To find the slope of a line perpendicular to this, we take the negative reciprocal of -4. The negative reciprocal is obtained by flipping the fraction and changing the sign.
The negative reciprocal of -4 is 1/4.
Now we have the slope of the line perpendicular to the given line, which is 1/4.
Next, we can use the point-slope form of a line to write the equation. The point-slope form is given by:
y - y1 = m(x - x1),
where (x1, y1) is the given point on the line, and m is the slope we determined (1/4).
Substituting the given point (4,7) and the slope (1/4) into the equation:
y - 7 = (1/4)(x - 4).
This is the equation of the line containing the point (4,7) and is perpendicular to the line 4x + y = 8.