Prove that the line PQ,with P(0;3) and Q(5;5),is parallel to the line 5y+5=2x
The slope of PQ is (5-3)/(5-0) = 2/5
That is also the slope of the given line.
So they are parallel.
To prove that line PQ (with point P(0, 3) and Q(5, 5)) is parallel to the line 5y + 5 = 2x, we need to compare the slopes of both lines and show that they are equal.
The slope-intercept form of a line is y = mx + b, where m represents the slope of the line. To determine the slope of line 5y + 5 = 2x, we can rewrite it in slope-intercept form:
5y + 5 = 2x
5y = 2x - 5
y = (2/5)x - 1
Comparing this equation to the standard form y = mx + b, we can see that the slope is m = 2/5.
Now let's find the slope of line PQ using the coordinates of points P(0, 3) and Q(5, 5). The slope (m) is calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates into the formula, we have:
m = (5 - 3) / (5 - 0)
m = 2 / 5
We can see that the slope of PQ is also 2/5, which is equal to the slope of the line 5y + 5 = 2x. Therefore, we can conclude that the line PQ is parallel to the line 5y + 5 = 2x.
y-y1=m(x-x1)
y-5=2/5(x-5)
y-5=2/5x-2
y=2/5x+3