What is the y-intercept of y =

2/3x + 2?

I have to write it out but how?

A line has a slope of
1/2 and passes through the point (0,5). What is the equation of the line?

A)y = 1/2x + 5

B)y = 1/2x - 5<---

C)y = 5x + 1/2

D)y = -5x + 1/2

Find an equation of the line that passes through the points (1,2) and (2,3).

A) y = x - 1
B) y = x + 1
C) y = x - 2 <--
D) y = 2x - 1

8)Find an equation of the line that has intercepts (1,0) and (0,4).
A) y = 4x - 1 <--
B) y = -4x + 4
C) y = -4x + 1
D) y = -4x - 4

9)A line passes through the point (2, 3) and has a slope of -2. Which is the equation of the line in point-slope form?

A) 2x + y = 7
B) y = -2x + 7
C) y - 3 = -2(x - 2)<---
D) y = -1/2x + 5

Y = (2/3)x + 2

x = 0 at the point where the graph crosses the y-axis. So in the Eq above, replace x with 0 and solve for y:

Y = (2/3)*0 * 2 = 0 + 2 = 2.
(x,y) = (0,2).

What is the y-intercept of y =

2/3x + 2?

I have to write it out but how?
------------------------------

The y axis intercept is where x = 0

which in this case is 2

and I think you meant to type
y = (2/3) x + 2
because what you typed was
y = 2/(3x) + 2
think parentheses when you try to express equations with a keyboard.

It's

y = two-thirds x + 2

its -2

2. Given: P(0,5), m = 1/2.

Y = mx + b = 5.
(1/2)*0 + b = 5, b = 5.
Eq: Y = (1/2)x + 5.

3. Given: (1,2), (2,3).
m = (3-2)/(2-1) = 1/1 = 1.
Y = mx + b = 2.
1*1 + b = 2, b = 1.
Eq: Y = x + 1.

8. Same procedure as #3.

9. Given: (2,3), (x,y), m = -2.
m = (y-3)/(x-2) = -2.
Cross multiply:
y-3 = -2(x-2).

To find the y-intercept of an equation, you need to set x equal to zero and solve for y. In the equation y = 2/3x + 2, when x is replaced with zero, the equation becomes y = 2/3(0) + 2, which simplifies to y = 2. Therefore, the y-intercept of the equation y = 2/3x + 2 is 2.

For the second question, to find the equation of a line given a point and slope, you can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) represents the given point and m represents the slope. In this case, the given point is (0,5) and the slope is 1/2. Plugging these values into the point-slope equation gives us y - 5 = 1/2(x - 0), which simplifies to y - 5 = 1/2x. Rearranging the equation, we get y = 1/2x + 5. Therefore, the equation of the line is y = 1/2x + 5.

For the third question, to find the equation of a line given two points, you can use the slope-intercept form of a linear equation: y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the given points are (1,2) and (2,3). We can first find the slope by using the formula m = (y2 - y1) / (x2 - x1) = (3 - 2) / (2 - 1) = 1. Now that we know the slope is 1, we can use one of the given points to substitute into the equation and solve for b. Using (1,2), we get 2 = 1(1) + b, which simplifies to 2 = 1 + b. Solving for b, we subtract 1 from both sides and get b = 1. Therefore, the equation of the line is y = x - 1.

For the fourth question, to find the equation of a line given the x-intercept and y-intercept, you can use the intercept form of a linear equation: x/a + y/b = 1, where a represents the x-intercept and b represents the y-intercept. In this case, the given intercepts are (1,0) and (0,4). Plugging these values into the equation, we get x/1 + y/4 = 1, which simplifies to x + y/4 = 1. Rearranging the equation, we get y/4 = 1 - x, and further simplifying gives y = 4(1 - x). Therefore, the equation of the line is y = -4x + 4.

For the last question, to find the equation of a line given a point and slope, you can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) represents the given point and m represents the slope. In this case, the given point is (2,3) and the slope is -2. Plugging these values into the point-slope equation gives us y - 3 = -2(x - 2), which simplifies to y - 3 = -2x + 4. Rearranging the equation, we get y = -2x + 7. Therefore, the equation of the line in point-slope form is y - 3 = -2(x - 2).