use the point slope form linear equation given to complete problem. y-3=3(x+1)what is the slope of the given line? what point does this line pass through, which is the basis of this equation?...

use the point slope form linear equation given to complete problem.

y-3=3(x+1)

what is the slope of the given line? what point does this line pass through, which is the basis of this equation? rewrite this equation in slope-intercept form. what is the y-intercept of this line? rewrite this equation in standard form. what is the x-intercept of this line? what is the equation in standaed form of a perpendicular line that passes through what was given. what is the x-intercept of the perpendicular line? what is the equation in standard form of a parallel line that passes through (0,-2)? on the parallel line, find the ordered pair where x=-2.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should arrange the terms of the given equation following the slope intercept form `y = mx + n` , to find the slope of the line.

Hence, you need to open the brackets such that:

`y - 3 = 3x + 3`

You need to isolate y to the left side such that:

`y = 3x + 3 + 3 => y = 3x + 6 `

Notice that the slope m of the given line is the coefficient of x such that:

`m = 3`

Hence, evaluating the slope of the given line yields `m = 3.`

Notice that you need to put the given equation in the slope intercept form to find the slope, hence, the slope intercept form is `y = 3x + 6` .

You need to know that the constant term that is present in the slope intercept form represents the y intercept, hence, the line intercepts y axis at y=6.

You should arrange the terms of the given equation following the  standard form Ax + By + C = 0 such that:

`3x - y + 6 = 0`

You should find x intercept of the line considering y = 0 such that:

`3x - 0 + 6 = 0 => 3x = -6 => x = -2`

Hence, the line intercepts x axis at x = -2.

You should know that you may find the equation of perpendicular line to the given line using the relation between the slopes of the lines such that:

`m_1*m_2=-1`

Considering `m_1 = 3 => m_2 = -1/3.`

You may find a point of intersection of lines using the equation of the given lines such that:

`x = 1 => y = 3 + 6 => y = 9`

Hence, the point (1,9) lies on both lines, hence, you may write the equation of perpendicular line such that:

`y - 9 = m_2*(x - 1) => y - 9 = (-1/3)(x-1)`

You may convert the point slope form of perpendicular line into the standard form of the equation of perpendicular line moving all terms to the left side such that:

`y - 9 + x/3 - 1/3 = 0 => x + 3y - 28 = 0`

You may find x intercept of perpendicular line considering y=0 such that:

`x = 28`

Hence, the perpendicular line intercepts x axis at x = 28.

You should know that you may find the equation of parallel line to the given line using the relation between the slopes of the lines such that:

`m_1 = m_3 => m_3 = 3`

Since the problem provides the information that the parallel line passes throught he point (0,-2), you should use the point slope form of equation such that:

`y - (-2) = 3(x - 0) => y + 2 = 3x`

Converting the slope intercept form of parallel line into the standard form yields `3x - y - 2 = 0` .

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