Question

1. Find the slope and the y-intercept of the equation 4x + 5y = -9.

2. Find the slope and the y-intercept of the equation y − 3(x − 1) = 0.

3. If a line with a slope of -2 crosses the y-axis at (0, 3), what is the equation of the line?

Answer 1

1. The slope is -4/5 and the y-intercept is (0, -9/5).

2. The slope is 3 and the y-intercept is (0,3).

3. The line is y=-2x+3.

Explanation:

To find the slope and y-intercept, convert the equation to y=mx+b where m=slope and b=y-intercept.

1. Convert the equation by rearranging the terms using inverse operations.

4x+5y=-9 Subtract 4x to both sides.

-4x -4x

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5y= -9 -4x Divide both sides by 5.

y= -9/5 - 4/5x

This is now in y=mx+b and m=-4/5 and b=-9/5.

2. Convert the equation by rearranging the terms using inverse operations.

y - 3(x-1)=0 Add 3(x-1) to both sides.

+3(x-1) +3(x-1)

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y = 3(x+1) Multiply 3 into the parenthesis.

y = 3x+3

This is now in y=mx+b and m=3 and b=3.

3. Write the equation of a line using point slope form

`y-y_1=m(x-x_1)`.

This becomes
`y-3=-2(x-0)\\y-3 = -2 (x)\\y-3 = -2x\\y= -2x+3`

Here m =-2 and b=3.