Straight line equations?

Question

A straight line has equation: 2y - 6x = 5
Find the gradient of the line, and also: the point (k, 6) lies on the line. Find the value of k

Answer 1

2y - 6x = 5

2y - 6x + 6x = 6x + 5

2y = 6x + 5

2y/2 = 6x/2 + 5/2

y = 3x + 2.5

The slope equals 3

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2y - 6x = 5

Point (k, 6)

2 ( 6 ) - 6k = 5

12 - 6k = 5

12 - 6k - 5 = 5 - 5

7 - 6k = 0

7 - 6k + 6k = 0 + 6k

7 = 6k

7 / 6 = 6k / 6

7 / 6 = k

1 1/6 = k

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Answer 2

you're able to locate the slope of the parallel line. known line equation is in the form of y = mx+b, the place m=slope 2x - 3y = 4 -3y = 4 - 2x -3y = -2x + 4 3y = 2x - 4 y = 2/3x - 4/3 m = 2/3 finding on the hot line equation, plug in the given factors and remedy the fee of the parallel slope. For (4,-2): y = mx + b -2 = (2/3)(4) + b remedy for b, which represents the y-intercept of the equation. -2 = 8/3 + b b = -2 - 8/3 b = -6/3 - 8/3 b = -14/3 Now you plug the slope and y-intercept into the equation sort. m = 2/3 b = -14/3 y = mx + b y = 2/3x + (-14/3) y = 2/3x - 14/3 answer examine -2 = (2/3)(4) - (14/3) -6/3 = 8/3 - 14/3 -6 = 8 - 14 -6 = -6 examine Mark

Answer 3

gradient is slope. Put into slope, intercept form:
2Y = 6X+5
Y = 3X +2.5
slope is 3.

12 = 6k + 5
k= 7/6

Answer 4

2y=6x+5
y=3x+5/2
gradient =slope=tan theta=6/2=3
sub(k,6)
12-6k=5
adding -12
-6k=-7
dividing by -6
k=7/6