Question

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.

Accepted Answer

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.

Answer

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.

Answer

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

Answer

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:

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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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