Question

Only questions 8 and 9 help please!!!

Answer 1

Answer:

Step-by-step explanation:

8) y = -2x + 1 and the line passes through (2, - 1)

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

y= -2x + 1

Comparing with the slope intercept form, slope = - 2

If two line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of that of the given line. Therefore, the slope of the line passing through (2,-1) is 1/2

To determine the intercept, we would substitute m = 1/2, x = 2 and y = -1 into y = mx + c. It becomes

- 1 = 1/2 × 2 + c = 1 + c

c = - 1 - 1 = - 2

The equation becomes

y = x/2 - 2

9) 3x + y = 5 and the line passes through (-9, 3)

The equation of the given line is

3x + y = 5

y = -3x + 5

Comparing with the slope intercept form, slope = - 3

If two line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of that of the given line. Therefore, the slope of the line passing through (- 9, 3) is 1/3

To determine the intercept, we would substitute m = 1/3, x = -9 and y = 3 into y = mx + c. It becomes

3 = 1/3 × -9 + c = - 3 + c

c = 3 + 3 = 6

The equation becomes

y = x/3 + 6

Answer 2

Answer:

Step-by-step explanation:

Perpendicular slopes are the opposite reciprocals of the slopes given.  Our slope in 8 is -2.  That means that the perpendicular slope is 1/2.  If the line goes through (2, -1), then

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

$y+1=\frac{1}{2}x-1$ and

$y=\frac{1}{2}x-2$

9 is a tiny bit trickier because we don't have the slope, the x term, on the opposite side of the equals sign from the y.  Let's do that and then we can determine the slope of that given line.  Moving over the 3x and isolating the y:

y = -3x + 5

So the slope is -3.  That means that the perpendicular slope is 1/3.  If the line goes through (-9, 3), then

$y-3=\frac{1}{3}(x-(-9))$ and

$y-3=\frac{1}{3}(x+9)$ and

$y-3=\frac{1}{3}x+3$ so

$y=\frac{1}{3}x+6$