Question

Please help me!!!

A. What is the slope of the given line?

B. What is the slope of the line perpendicular to the given line?

C. What is the slope of the line that is parallel to the given line?

D. Find the equation of the line that is perpendicular to the given line and passes through the point (-1, 2).

E. What is the y-intercept of the equation from part (D)?

Answer 1

a. Slope is defined by rise/run. It looks like the points where it intersects the axes are at (0, 6) and (2, 0)
Basically you take (y-y1)/(x-x1), which in this case could be (6-0)/(0-2), which is -3.
b. The perpendicular slope would be the negative inverse of that.
The inverse of 3 is 1/3, so the negative inverse of -3 would also be 1/3.
c. The parallel slope is the same as the original slope.
d. Plug these points in for y=mx+b. 
2=(1/3)(-1)+b
2=-1/3+b
b=7/3. (that's 2 and 1/3).
The equation for that line would be y=(1/3)x+(7/3)
e. The y intercept is found when x=0. But it's also the b in the y=mx+b equation, so the y intercept is (0, 7/3).

In case that's hard to read:
a. Slope = -3
b. Perpendicular Slope = 1/3
c. Parallel Slope = -3
d. y=(1/3)x+(7/3)
e. Y intercept = (0,, 7/3)

Hope that helps!

Answer 2

Answer:

A. -3

B. 1/3

C. -3

D. $y=\frac{1}{3}(x)+\frac{7}{3}$

E. 7/3

Step-by-step explanation:

If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$, then the slope of the line is

$m=\frac{y_2-y_1}{x_2-x_1}$

Part A:

From the given figure it is clear that the line passes through the point (0,6) and (2,0). So the slope of the given line is

$m=\frac{0-6}{2-0}=-3$

Therefore the slope of given line is -3.

Part B:

Product of slopes of two perpendiculars line is equal to -1.

Let the slope of perpendicular line be m.

$m\times (-3)=-1$

Divide both sides by -3.

$m=\frac{-1}{-3}$

$m=\frac{1}{3}$

Therefore the slope of the line perpendicular to the given line is 1/3.

Part C:

Slopes of two parallel lines are same.

Therefore the slope of the line that is parallel to the given line is -3.

Part D:

If a line passes through two points $(x_1,y_1)$ with slope m, then the point slope form of the line is

$y-y_1=m(x-x_1)$

The perpendicular line passes through the point (-1,2) and slope of that line is 1/3.

$y-2=\frac{1}{3}(x-(-1))$

$y-2=\frac{1}{3}(x)+\frac{1}{3}$

Add 2 on both sides.

$y=\frac{1}{3}(x)+\frac{1}{3}+2$

$y=\frac{1}{3}(x)+\frac{7}{3}$

Therefore the equation of the line that is perpendicular to the given line and passes through the point (-1, 2) is $y=\frac{1}{3}(x)+\frac{7}{3}$.

Part E:

Equation of part D is

$y=\frac{1}{3}(x)+\frac{7}{3}$

Substitute x=0 to find the y-intercept.

$y=\frac{1}{3}(0)+\frac{7}{3}$

$y=\frac{7}{3}$

Therefore the y-intercept is 7/3.