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Sagot :
The question is incomplete.
However, from the given parameters, a likely question could be to:
1. Write an equation in slope intercept form through (20,-8) and is parallel to 7x - 4y = -5
or
2. Write an equation in slope intercept form through (20,-8) and is perpendicular to 7x - 4y = -5
Answer:
See Explanation
Step-by-step explanation:
First, we calculate the slope of [tex]7x - 4y = -5[/tex]
[tex]7x - 4y = -5[/tex]
Subtract 7x from both sides
[tex]7x-7x - 4y = -5-7x[/tex]
[tex]- 4y = -5-7x[/tex]
Make y the subject
[tex]\frac{- 4y}{-4} = \frac{-5-7x}{-4}[/tex]
[tex]y = \frac{-5-7x}{-4}[/tex]
[tex]y = \frac{5+7x}{4}[/tex]
[tex]y = \frac{5}{4}+\frac{7}{4}x[/tex]
[tex]y = \frac{7}{4}x+\frac{5}{4}[/tex]
The general format of an equation is:
[tex]y= mx + b[/tex]
Where
[tex]m = slope[/tex]
By comparison:
[tex]m = \frac{7}{4}[/tex]
Solving (1): Parallel
Here, we assume that the line is parallel to the given equation.
And as such, it means that they have the same slope
So, we have:
[tex](x_1,y_1) = (20,-8)[/tex]
and
[tex]m = \frac{7}{4}[/tex]
The equation is then calculated as:
[tex]y - y_1 = m(x - x_1)[/tex]
This gives:
[tex]y - (-8) = \frac{7}{4}(x - 20)[/tex]
[tex]y +8 = \frac{7}{4}(x - 20)[/tex]
Open bracket
[tex]y +8 = \frac{7}{4}x - \frac{7}{4}*20[/tex]
[tex]y +8 = \frac{7}{4}x - 7*5[/tex]
[tex]y +8 = \frac{7}{4}x - 35[/tex]
Make y the subject
[tex]y = \frac{7}{4}x - 35-8[/tex]
[tex]y = \frac{7}{4}x -43[/tex]
Solving (2): Perpendicular
Here, we assume that the line is perpendicular to the given equation.
And as such, it means that the following relationship exists between their slope:
[tex]m_2 = -\frac{1}{m_1}[/tex]
Where
[tex]m_1 =m =\frac{7}{4}[/tex] -- as calculated above
Substitute 7/4 for m1 in [tex]m_2 = -\frac{1}{m_1}[/tex]
[tex]m_2 = -\frac{1}{7/4}[/tex]
[tex]m_2 = -\frac{4}{7}[/tex]
So, we have:
[tex](x_1,y_1) = (20,-8)[/tex]
and
[tex]m_2 = -\frac{4}{7}[/tex]
The equation is then calculated as:
[tex]y - y_1 = m(x - x_1)[/tex]
This gives:
[tex]y - (-8) = -\frac{4}{7}(x - 20)[/tex]
[tex]y +8 = -\frac{4}{7}(x - 20)[/tex]
Open bracket
[tex]y +8 = -\frac{4}{7}x + \frac{4}{7}*20[/tex]
[tex]y +8 = -\frac{4}{7}x + \frac{80}{7}[/tex]
Make y the subject
[tex]y = -\frac{4}{7}x + \frac{80}{7}-8[/tex]
[tex]y = -\frac{4}{7}x + \frac{80-56}{7}[/tex]
[tex]y = -\frac{4}{7}x + \frac{24}{7}[/tex]
Take LCM
[tex]y = \frac{-4x + 24}{7}[/tex]
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