What is the equation of the line with slope m=-4 m=4 that passes through (4,5) (4,5)?

3 Answers
May 11, 2018

4x+y-21=04x+y21=0

Explanation:

Using point gradient formula:

(y-y_1)=m(x-x_1)(yy1)=m(xx1)
where (x_1,y_1)(x1,y1) is (4,5)(4,5)

(y-5)=-4(x-4)(y5)=4(x4)
y-5=-4x+16y5=4x+16
4x+y-21=04x+y21=0

May 11, 2018

y=-4x+21y=4x+21

Explanation:

m=-4m=4 is equivalent to the gradient by y=mx+cy=mx+c. The coordinates (5,4)(5,4) indicates that the point occurs when x=5x=5 and y=4y=4 and these are free variables that you can plug in for xx and yy.

Using the format of y=mx+cy=mx+c solve for cc:

y=mx+cy=mx+c
5=-4(4)+c5=4(4)+c
5=-16+c5=16+c
5+16=c5+16=c
c=21c=21

Therefore, the equation for the slope is:

y=-4x+21y=4x+21

May 11, 2018

Equation of the line is 4 x + y =21 4x+y=21

Explanation:

The equation of line passing through (x_1=4,y_1=5)(x1=4,y1=5) having

slope of m=-4m=4 is y-y_1=m(x-x_1) ; yy1=m(xx1);

:. y-5= -4 (x-4) or y-5 = -4 x +16 or

4 x + y =21 ;

Equation of the line is 4 x + y =21 ; [Ans]