Use the point slope form line equation y+4=-4(x-2).  what point does this line pass through. Rewrite this equation in slope-intercept form. What is the x-intercept of this line.

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flbyrne's profile pic

flbyrne | (Level 3) Assistant Educator

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The slope of a line is defined as the change in y divided by the change in x:

Slope=`(Deltay)/(Deltax)`

Given a point `(x_1,y_1)`, the change in y can be written as

`Deltay=y-y_1`

And the change in x can be written as:

`Deltax=x-x_1`

The equation of the line can then be written:

`y-y_1=(Slope)(x-x_1)`

In `y-(-4)=-4(x-2)` the point `(x_1,y_1)` is equal to (2,-4) and the slope is equal to -4.

Therefore the line passes through the point (2,-4) and this point is the basis of this equation.

The slope intercept form is y=mx+b, where m is the slope and b is the y intercept. To write the slope intercept method, solve for y.

`y+4=-4(x-2)`

`y=-4x+8-4`

`y=-4x+4`             (1)

Thus the slope is -4 and the y intercept is 4.

The standard form of a line is: ax+by=c. Add 4x to both sides of (1).

`4x+y=4`

To determine the x intercept, substitute 0 for y.

`4x=4`

`x=1`

Thus the x intercept is 1.

Graph:

 

 

 

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of the line y + 4 = -4*(x - 2) is in the point slope form. Rewriting the equation `(y+4)/(x - 2) = -4` . The slope of this line is -4 and it passes through the point (2, -4).

y + 4 = -4*(x - 2)

=> y + 4 = -4x + 8

=> y = -4x + 4

This is the equation in the slope-intercept form.

At the x-intercept the y-coordinate is 0.

0 = -4x + 4

=> x = 1

The x-intercept of the line is 1.

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The equation of a line through (a,b) with slope m is given by (y - b)/(x - a) = m

The equation of the line that is given can be rewritten in this form.

y + 4 = -4*(x - 2)

(y + 4)/(x - 2) = -4

This line passes through the point (2, -4).

In slope intercept form this line has an equation of the form y = mx + c

y + 4 = -4*(x -2 )

y + 4 = -4x + 8

y = -4x + 4

At the x-intercept, the y-coordinate is 0.

0+ 4 = -4*x + 8

-4*x = -4

x = 1

The x-intercept is 1.

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

y+4=-4(x-2)

Recall the point slope formula: 

y - y1 = m(x - x1) where m is the slope and (x1,y1) is a point. 

Realize that y1 = -4 and x1 = 2 so a point that this line goes through is (2, -4)

To get this into slope intercept, just distribute the -4 and solve for y like this: 

y + 4 = -4x + 8

y + -4x + 8 - 4

y = -4x + 4    Done!

The x-intercept means the y value is 0 so plug that in and solve for x: 

0 = -4x + 4

x = -4/-4 = 1

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