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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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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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.
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.
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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