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A line of slope - 7 intersects the curve given by
y = (x - 4)(x + 1) at a point with x-coordinate 1.
Which of the following is an equation of the line?

Sagot :

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The equation of the line will be y=-7x+1 which is intersecting the curve  y = (x - 4)(x + 1) .

What is slope?

Slope of a line is the measure of the steepness and the direction of the line. It can be calculated using any two points lying on the line.

We know that the equation of line is given as:

[tex]y=mx+c[/tex]

Here m is slope of the line.

m=-7

Since the line is intersecting the curve

[tex]y=(x-4)(x+1)[/tex]

The line is intersecting the curve at the x coordinate 1 so this point will satisfy both the equations.

So the equation if line will be

[tex]y=(-7)(1)+c[/tex]

[tex]y=-7+c[/tex]

Now from the equation of the curve.

[tex]y=(1-4)(1+1)=(-3)(2)=-6[/tex]

putting the value of y in the equation.

[tex]-6=-7+c[/tex]

[tex]c=1[/tex]

Now the equation of the line is

[tex]y=mx+c\\\\\\y=(-7x +1)[/tex]

Hence the Slope of a line is the measure of the steepness and the direction of the line. It can be calculated using any two points lying on the line.

To know more about the Line equation follow

https://brainly.com/question/1884491

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