Pergunta

4x Write an equation of the line that is parallel to 5x+20y=10 and passes through the point (8,3) A y=4x-29 B y=4x+35 C y=(1)/(4)x-1 D y=-(1)/(4)x+3 E y=-(1)/(4)x+5
Solução

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BrunaProfissional · Tutor por 6 anos
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The equation of the line that is parallel to and passes through the point (8,3) is , which corresponds to option E.
Explicação
## Step 1
The given equation of the line is . We need to convert this equation into the slope-intercept form, which is , where is the slope of the line and is the y-intercept.
## Step 2
To convert the given equation into slope-intercept form, we divide the entire equation by 20. This gives us .
## Step 3
The slope of the given line is . Since parallel lines have the same slope, the slope of the line we are looking for is also .
## Step 4
We are given a point (8,3) that lies on the line we are looking for. We can use the point-slope form of a line equation, which is , where is a point on the line and is the slope.
## Step 5
Substituting the given point and slope into the point-slope form gives us .
## Step 6
Solving this equation for gives us the equation of the line in slope-intercept form: .
The given equation of the line is . We need to convert this equation into the slope-intercept form, which is , where is the slope of the line and is the y-intercept.
## Step 2
To convert the given equation into slope-intercept form, we divide the entire equation by 20. This gives us .
## Step 3
The slope of the given line is . Since parallel lines have the same slope, the slope of the line we are looking for is also .
## Step 4
We are given a point (8,3) that lies on the line we are looking for. We can use the point-slope form of a line equation, which is , where is a point on the line and is the slope.
## Step 5
Substituting the given point and slope into the point-slope form gives us .
## Step 6
Solving this equation for gives us the equation of the line in slope-intercept form: .
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