Answer:
y = (1/3)x + 7
Step-by-step explanation:
The general structure form of a line in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept.
The slope of a perpendicular line is the opposite-signed, reciprocal of the original line's slope. Therefore, if the slope of the original line is m = -3, the new slope is m = 1/3.
The y-intercept can be found by plugging the new slope and the values from the point (-3, 6) into the slope-intercept form equation.
m = 1/3
x = -3
y = 6
y = mx + b <----- Slope-intercept form
6 = (-3)(1/3) + b <----- Insert values
6 = -1 + b <----- Multiply -3 and 1/3
7 = b <----- Add 1 to both sides
Now, that you have the slope and y-intercept, you can construct the equation of the perpendicular line.
y = (1/3)x + 7
Answer:
125.7
I got this one right on my test yesterday :)
Answer:
Step-by-step explanation:
15 x 7 = 105
The gap is either 9 x 7 =63 or 12 x 7 = 84
105 - 84 = 21
105 - 63 = 42
So the shaded area is either is 21 or 42
Answer:
65 square units
Step-by-step explanation:
Assuming point O refers to the origin, the segment OA has slope ...
m = Δy/Δx = 5/1 = 5
Then the slope of the perpendicular line AP will be the negative reciprocal of this, -1/5.
The x-intercept of the line through (1, 5) with slope -1/5 can be found by setting y=0 in the point-slope equation for that line:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
0 -5 = (-1/5)(x -1)
25 = x -1 . . . . . . . multiply by -5
x = 26 . . . . . . . add 1
This means ΔOAP has a base length (OP) of 26 units and an altitude of 5 units. Its area is given by the formula ...
A = 1/2bh
A = 1/2(26)(5) = 65 . . . . square units
Triangle OAP has an area of 65 square units.
