Write the equation of a line in slope-intercept form that is perpendicular to the line y= 3/5 x - 1 and passes through the point (-9, 4). write the equation of a line in slope-intercept form passing through (4, 5) and (6, 8)

3) Option C

4) Option C

Step-by-step explanation:

Question 3:

A line perpendicular to another line has a slope which is a negative reciprocal of the line which is perpendicular to it.

So the slope of its perpendicular line will be .

The standard slope intercept form of an equation of a line is .

Therefore, the equation of a line perpendicular to the given equation is

Question 4:

Therefore, the equation of a line passing through (4, 5) and (6, 8) is

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simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .