The equation in slope intercept form is y = 2/3x + 14/3 and the equation in point slope form is y - 6 = 2/3(x - 2)
The equation of the line is given as:
3y + 7 = 2x
Subtract 7 from both sides
3y = 2x - 7
Divide both sides by 3
y = 2/3x - 7/3
Both lines are parallel.
So, they have the same slope
This means that the slope of the line is:
m = 2/3
The point slope form of a linear equation is represented as:
y - y1 = m(x - x1)
The line is said to pass through the point (2,6).
This means that (x1,y1) = (2,6)
Substitute (x1,y1) = (2,6) and m = 2/3 in the equation y - y1 = m(x - x1)
This gives
y - 6 = 2/3(x - 2)
Add 6 to both sides
y = 2/3(x - 2) + 6
Expand
y = 2/3x - 4/3 + 6
Evaluate the sum and difference
y = 2/3x + 14/3
Hence, the equation in slope intercept form is y = 2/3x + 14/3 and the equation in point slope form is y - 6 = 2/3(x - 2)
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