Question
Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible.
Through (7, 3) and (3, 7)
____
What is the equation of the line? (Simplify your answer.)
Through (7, 3) and (3, 7)
____
What is the equation of the line? (Simplify your answer.)
Answers
GPT 3.5
To find the equation of the line, we can use the formula for finding the slope of a line:
m = (y2 - y1)/(x2 - x1)
Using the coordinates (7, 3) and (3, 7), we can substitute the values into the formula:
m = (7 - 3)/(3 - 7)
m = 4/-4
m = -1
Now that we have the slope, we can use the point-slope form of a line to write the equation:
y - y1 = m(x - x1)
Using the point (7, 3) as our point (x1, y1), we substitute the values:
y - 3 = -1(x - 7)
Simplifying the equation, we get:
y - 3 = -x + 7
Adding x to both sides:
y = -x + 7 + 3
Simplifying further, we get the equation in slope-intercept form:
y = -x + 10
m = (y2 - y1)/(x2 - x1)
Using the coordinates (7, 3) and (3, 7), we can substitute the values into the formula:
m = (7 - 3)/(3 - 7)
m = 4/-4
m = -1
Now that we have the slope, we can use the point-slope form of a line to write the equation:
y - y1 = m(x - x1)
Using the point (7, 3) as our point (x1, y1), we substitute the values:
y - 3 = -1(x - 7)
Simplifying the equation, we get:
y - 3 = -x + 7
Adding x to both sides:
y = -x + 7 + 3
Simplifying further, we get the equation in slope-intercept form:
y = -x + 10
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