What is the distance from the origin to point P graphed on the complex plane below?

1) Find an equation of the line that passes through the point and has the indicated slope m. (Let x be the independent variable

VMariaS [17]

Answer:

1) The equation of a line is $y=-\frac{1}{2}x+\frac{17}{2}$ .

2) The equation of the line that passes through the points (2,4) and (3,7) is $y=3x-2$

3) The equation of the line that has slope m = −2 and y-intercept equal to -1 is $y=-2x-1$

4) The slope-intercept form of $y-7=0$ is $y=7$ , where the slope is zero and the y-intercept is (0, 7).

Step-by-step explanation:

1) The equation of a line with slope m, passing through the point $(x_1,y_1)$ , is

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

We know that $m = -\frac{1}{2}$ and the point is (1,8). Therefore, the equation of the line is

$y-8=-\frac{1}{2} (x-1)\\\\y-8+8=-\frac{1}{2}\left(x-1\right)+8\\\\y=-\frac{1}{2}x+\frac{1}{2}+8\\\\y=-\frac{1}{2}x+\frac{17}{2}$

2) The equation of a line is typically written as

$y=mx+b$

where m is the slope and b is the y-intercept.

The slope of a line is a measure of how fast the line "goes up" or "goes down" and is given by

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

To find the equation of the line that passes through the points (2, 4) and (3, 7), the first step is to find the slope.

Applying the definition of the slope, we get that

$m=\frac{7-4}{3-2}=3$

Now, we find the y-intercept with the help of point (2, 4) and the general form of the equation of a line

$4=3(2)+b\\b=-2$

The equation of the line that passes through the points (2,4) and (3,7) is $y=3x-2$

3) The equation of the line that has slope m = −2 and y-intercept equal to -1 is

$y=-2x-1$

4) The slope-intercept form of $y-7=0$ is $y=7$ , where the slope is zero and the y-intercept is (0, 7).

3 0

3 years ago

Working together, two people can cut a large lawn in 44 hr. One person can do the job alone in 1 hr less than the other. How lo

SVETLANKA909090 [29]

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5 0

3 years ago

on a test, laura completes the expressions shown. 4^3 x 3^5 = 12^8. what mistake did she make and what is the correct expression

MAVERICK [17]

4^3= 4*4*4=64. 3^5= 3*3*3*3*3=243. 64*243=15,552. 12^8= 12*12*12*12*12*12*12*12= 429,981,696. 15,552≠429,981,696.

5 0

3 years ago

Kelly gets paid $68 for watching her neighbors dogs for 10 days how much does kelly earn per day

galina1969 [7]

She earns $6.80 per day :-)

4 0

3 years ago

Read 2 more answers

What is the circumference of a QUATER CIRCLE if the radius of the quater circle is 2CM

MissTica

To find the area of a quarter circle, you simply take a quarter of a full circle. As all quarters are equal, this means that the formula would be πr24πr24. But wait, there's more. If you notice, πr24=πr22πr24=πr22. This coincides with the circle formula, just with half the radius. Notice anything? A quarter of a circle can be calculated in the same way a circle a quarter the size can. This means that a quarter circle is equal to a circle a quarter size. In this same way, a ninth of a circle is equal to a circle of one ninth the size.

8 0

3 years ago