in questions 1 and 2, write an equation of the line in slope-intercept form.

1. the slope is -4/3; the y-intercept is -2.
2. the slope is 0; the y-intercept is -5.

my answers:
1.y=-4/3-2
2. y=-5
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write an equation of the line that passes through the point and has the given slope. write the equation in slope-intercept form.
3. (4,-5), m=2/3
4. (-4,3), m=-3/4
5. (2,-3), m=2/6
6. (-4,3), m=-8/7

my answers:
3. y=2/3x-23/3
4. y=-3/4x
5. y=2/6x-4/5
6. y=-8/7x-11/7

please correct them if they're not right and tell me how.. thanks! xx

1.y=-4/3x-2

5. y=2/6x - 11/3

1. To write the equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, you plug in the given values of slope and y-intercept.

For the first question, the slope is -4/3 and the y-intercept is -2. Plugging these values into the equation, you get:
y = (-4/3)x - 2.

Your answer is correct.

2. For the second question, the slope is 0 and the y-intercept is -5. Plugging these values into the equation, you get:
y = 0x - 5, which simplifies to y = -5.

Your answer is correct.

3. In order to write an equation of a line that passes through a given point (x₁, y₁) and has a given slope m, you can use the point-slope form of the equation:
y - y₁ = m(x - x₁).

For the third question, the given point is (4, -5), and the slope is 2/3. Plugging these values into the point-slope form, you get:
y - (-5) = (2/3)(x - 4).
Simplifying, you can write it in slope-intercept form:
y = (2/3)x - 8/3.

Your answer is correct.

4. Similarly, for the fourth question, the given point is (-4, 3), and the slope is -3/4. Plugging these values into the point-slope form, you get:
y - 3 = (-3/4)(x - (-4)).
Simplifying, you can write it in slope-intercept form:
y = (-3/4)x - 9/4.

Your answer is correct.

5. For the fifth question, the given point is (2, -3), and the slope is 2/6. Plugging these values into the point-slope form, you get:
y - (-3) = (2/6)(x - 2).
Simplifying, you can write it in slope-intercept form:
y = (2/6)x + (4/3) - (9/3).
Further simplifying, you get: y = (2/6)x - (5/3).

Your answer is almost correct, but the constant term should be written as -5/3 instead of -4/5.

6. Lastly, for the sixth question, the given point is (-4, 3), and the slope is -8/7. Plugging these values into the point-slope form, you get:
y - 3 = (-8/7)(x - (-4)).
Simplifying, you can write it in slope-intercept form:
y = (-8/7)x + 32/7.

Your answer is correct.

Overall, your answers are mostly correct. Just make sure to double-check any arithmetic or simplifications, and you'll be good to go!