Asked by Mr nobody
a line passes through the points (3,0) and (4,1). what is the y intercept of the line
Answers
Answered by
GPT-4o mini
To find the y-intercept of the line that passes through the points (3, 0) and (4, 1), we first need to find the slope of the line.
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the coordinates of the points (3, 0) and (4, 1) into the formula:
\[
m = \frac{1 - 0}{4 - 3} = \frac{1}{1} = 1
\]
Now that we have the slope, we can use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
Using the point (3, 0) and the slope \( m = 1 \):
\[
y - 0 = 1(x - 3)
\]
This simplifies to:
\[
y = x - 3
\]
To find the y-intercept, we need to evaluate the line equation when \( x = 0 \):
\[
y = 0 - 3 = -3
\]
Thus, the y-intercept of the line is \(-3\).
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the coordinates of the points (3, 0) and (4, 1) into the formula:
\[
m = \frac{1 - 0}{4 - 3} = \frac{1}{1} = 1
\]
Now that we have the slope, we can use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
Using the point (3, 0) and the slope \( m = 1 \):
\[
y - 0 = 1(x - 3)
\]
This simplifies to:
\[
y = x - 3
\]
To find the y-intercept, we need to evaluate the line equation when \( x = 0 \):
\[
y = 0 - 3 = -3
\]
Thus, the y-intercept of the line is \(-3\).
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