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The line has a slope 5 / 4 and passes through ( − 3, 4 ). What is the equation of the line ? Select one: a. 4x + 5y + 31 = 0 b. 5x − 4y + 31 = 0 c. 4x − 5y + 31 = 0 d. 5x − 4y − 31 = 0

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Answer:

b: 5x-4y+31=0

Explanation:

Let's look for an equation of the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

We are given the slope, m, as (5/4), so we can write: y = (5/4)x+b.

To find b, just enter the given point, (-3,4), into the above equation and solve for b:

y=(5/4)x + b

4=(5/4)(-3) + b for (-3,4)

4 = -(15/4)+b

4 + (15/4) = b

4 + (3 3/4) = b

b = 7 3/4

The equation becomes y = (5/4)x + 7 3/4

Also written as: y = (5/4)x + (31/4)

To match this with one of the options, let's multiply by 4 to remove the two fractions:

y = (5/4)x + (31/4)

4y = (5)x + (31)

Rearrange so that the expression is = 0:

4y-5x-31 = 0

Now multiply by -1: -4y+5x+31=0

Rearrange and this will match option b: 5x-4y+31=0

User DanSingerman
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