Question

Please help me!!!

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.