The slope of the first equation has a slope of one and a y intercept of -4. The second equation has a y intercept of -2.3333 as seen when plugging in 0 for x, so the same y-intercept and same line are out of the question. This means either they have the same slope and thus are parallel or intersect at some point. A simple way to find out? Plug in 1 for x on the second. If it isn't -1.33333, which is a slope of positive 1 such as in the first equation, they WILL INTERSECT somewhere. When plugging in 1, we get
3y - 1 = -7
3y = -6
y = -2
(1, -2) is the next point after (0, -2.3333)
That means it is most certainly not the same slope, and thus they will intersect at some point. The two slopes are 1/1 and 1/3 if you weren't aware.
<u>Answer:</u>
Standard form of a line passing through (-2, 4) and having slope of -1/7 is x + 7y = 26
<u>Solution:</u>
Given that we need to determine standard form of a line that goes through (-2 , 4) and slope of the line is -1/7
Standard form of line passing through point ( a , b ) and having slope m is given by
(y – b) = m ( x – a) --------(1)
In our case given point is ( -2 , 4 ) and slope is -1/7 that means
a = -2 , b = 4 , m = -(1/7)
On substituting given value of a , b and m is equation (1) we get


=> 7( y - 4 ) = -x – 2
=> 7y + x = -2 + 28
=> x + 7y = 26
Hence standard form of a line passing through (-2,4) and having slope of –(1/7) is x + 7y = 26
The answer would be 24 pints