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 5x + 20y = 10 and passes through the point (8,3) is y = -\frac{1}{4}x + 5, which corresponds to option E.
Explicação
## Step 1
The given equation of the line is 5x + 20y = 10. We need to convert this equation into the slope-intercept form, which is y = mx + b, where m is the slope of the line and b 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 y = -\frac{1}{4}x + \frac{1}{2}.
## Step 3
The slope of the given line is -\frac{1}{4}. Since parallel lines have the same slope, the slope of the line we are looking for is also -\frac{1}{4}.
## 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 y - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.
## Step 5
Substituting the given point and slope into the point-slope form gives us y - 3 = -\frac{1}{4}(x - 8).
## Step 6
Solving this equation for y gives us the equation of the line in slope-intercept form: y = -\frac{1}{4}x + 5.
The given equation of the line is 5x + 20y = 10. We need to convert this equation into the slope-intercept form, which is y = mx + b, where m is the slope of the line and b 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 y = -\frac{1}{4}x + \frac{1}{2}.
## Step 3
The slope of the given line is -\frac{1}{4}. Since parallel lines have the same slope, the slope of the line we are looking for is also -\frac{1}{4}.
## 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 y - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.
## Step 5
Substituting the given point and slope into the point-slope form gives us y - 3 = -\frac{1}{4}(x - 8).
## Step 6
Solving this equation for y gives us the equation of the line in slope-intercept form: y = -\frac{1}{4}x + 5.
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