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.

Expert Answers

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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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