# How do I find the following equations for the y=mx+b form: a) m=-4/7 and through (3,0) b) passing through (3,2) and parallel to 3x-5y=6 c)(-2,2) and perpendicular to 4x-5y=5. Thank youHow do I find...

How do I find the following equations for the y=mx+b form:

a) m=-4/7 and through (3,0)

b) passing through (3,2) and parallel to 3x-5y=6

c)(-2,2) and perpendicular to 4x-5y=5.

Thank you

How do I find the following equations of the line with a given slope and passing through a given point y=mx+b form:

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I edited the question to divide it into what I thought were the correct parts. If this isn't correct, please let me know.

For part a, we know the value of m and can plug in the point 3,0 to find the value of the y-intercept (b).

y = mx + b

0 = (-4/7)(3) + b

0 = -12/7 + b

b = 12/7

b) passing through (3,2) and parallel to 3x-5y=6

If two lines are parallel, they will have the same slope. Start by rearranging the equation to the line form and find the value of the slope.

3x - 5y = 6

-5y = -3x + 6

y = 3/5 x - 6/5

Slope = 3/5 which can be substituted into the line equation with the point (3,2) to find the y-intercept

2 = 3/5(3) + b

2 = 9/5 + b

2 - 9/5 = b

b = 1/5

c)(-2,2) and perpendicular to 4x-5y=5.

Part c is very similar to b only the slope of the perpendicular line will be the inverse of the slope in the original equation.

4x - 5y = 5

-5y = -4x + 5

y = 4/5 x - 1

Slope = 4/5 so the line perpendicular to this one will have a slope of 5/4

y = 5/4 x + b to which we can plug in the data point (-2,2)

2 = 5/4(-2) + b

2 = -10/4 + b

b = 2 + 10/4

b = 18/4 = 9/2