Question
Write the slope-intercept form of the line that passes through the point (1,0) and is parallel to x - y=7
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GPT 3.5
To find the slope-intercept form of the line, we need to find the slope of the given line first.
The equation x - y = 7 can be rewritten in slope-intercept form by isolating y on one side of the equation:
x - y = 7
-y = -x + 7
y = x - 7
By comparing this equation to y = mx + b, where m represents the slope, we can see that the slope of the given line is 1.
Since the line we are looking for is parallel to the given line, it will also have a slope of 1.
Now that we have the slope, we can use the point-slope form to find the equation of the line. The point-slope form is:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents the point on the line and m represents the slope.
Using the point (1,0), we have:
y - 0 = 1(x - 1)
y = x - 1
Therefore, the slope-intercept form of the line that passes through the point (1,0) and is parallel to x - y = 7 is y = x - 1.
The equation x - y = 7 can be rewritten in slope-intercept form by isolating y on one side of the equation:
x - y = 7
-y = -x + 7
y = x - 7
By comparing this equation to y = mx + b, where m represents the slope, we can see that the slope of the given line is 1.
Since the line we are looking for is parallel to the given line, it will also have a slope of 1.
Now that we have the slope, we can use the point-slope form to find the equation of the line. The point-slope form is:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents the point on the line and m represents the slope.
Using the point (1,0), we have:
y - 0 = 1(x - 1)
y = x - 1
Therefore, the slope-intercept form of the line that passes through the point (1,0) and is parallel to x - y = 7 is y = x - 1.
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