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neonofarm [45]
3 years ago
14

Write the equation of the line in slope-intercept form (y=mx+b) that has the slope m=2 and a y-intercept (0,4)

Mathematics
1 answer:
Bas_tet [7]3 years ago
7 0

Answer:

The equation is

y = 2 x + 4

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Write the equation of the line that is perpendicular to 3x + 7y = 15 and passes through (4, 9)
k0ka [10]

Answer:

7x - 3y = 1

Step-by-step explanation:

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y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x + 7y = 15 into this form

Subtract 3x from both sides

7y = - 3x + 15 ( divide all terms by 7 )

y = - \frac{3}{7} x + \frac{15}{7} ← in slope- intercept form

with slope m = - \frac{3}{7}

Given a line with slope m the the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{-\frac{3}{7} } = \frac{7}{3}, thus

y = \frac{7}{3} x + c ← is the partial equation of the line

To find c substitute (4, 9) into the partial equation

9 = \frac{28}{3} + c ⇒ c - \frac{1}{3}

y = \frac{7}{3} x - \frac{1}{3} ← in slope- intercept form

Multiply through by 3

3y = 7x - 1 ( subtract 3y from both sides )

0 = 7x - 3y - 1 ( add 1 to both sides )

1 = 7x - 3y, that is

7x - 3y = 1 ← in standard form

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3 years ago
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