Determine the equation of the line described by the given information.
a) slope -2/3, passing through (0,6)
b) passing through points (2,7) and (6,11)
c) parallel to y=4x-6 passing through point (2,6)
a) We use the slope-point formula
y-y1 = m (x - x1)
y - 6 = -2/3(x - 0)
y - 6 = -2/3x + 0
y = -2/3x + 6
b) first we found the slope using the two points
m = y2 - y1 / x2 - x1
m = 11 - 7 / 7 - 2
m = 4 / 5
then use the point-slope formula as in (a) to find the equation
c) We know that in order for two lines two be
parallel they must to have the same slope.
So, the slope in the given equation is m = 4
Now, by taken m = 4 and the point (2, 6) and using
again the point-slope formula as in example (a) we find the equation.
Good teaching, Chemath.
Thank you~~
a) To determine the equation of the line, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
In this case, the slope is -2/3 and the given point is (0,6). Plugging these values into the point-slope form, we get:
y - 6 = (-2/3)(x - 0)
Simplifying, we have:
y - 6 = (-2/3)x
Further simplifying, we obtain the equation of the line:
y = (-2/3)x + 6
So, the equation of the line is y = (-2/3)x + 6.
b) We can use the two-point form of a linear equation to determine the equation of the line passing through the given points:
y - y1 = (y2 - y1)/(x2 - x1)(x - x1)
where (x1, y1) and (x2, y2) are the given points.
Let's use the points (2,7) and (6,11). Plugging these values into the two-point form, we get:
y - 7 = (11 - 7)/(6 - 2)(x - 2)
Simplifying, we have:
y - 7 = (4/4)(x - 2)
Further simplifying, we obtain the equation of the line:
y - 7 = x - 2
Adding 7 to both sides, we get:
y = x + 5
So, the equation of the line is y = x + 5.
c) The line is parallel to y=4x-6 and passes through the point (2,6).
Parallel lines have the same slope, so the slope of the line we are looking for is 4.
Using the point-slope form, we can plug in the slope of 4 and the given point (2,6):
y - 6 = 4(x - 2)
Simplifying, we have:
y - 6 = 4x - 8
Adding 6 to both sides, we get:
y = 4x - 2
So, the equation of the line is y = 4x - 2.