How to find the y-intercept when given two points?
Understand the Problem
The question is asking how to calculate the y-intercept of a line given two points on that line. The high-level approach involves using the two points to determine the slope of the line and then applying the slope-intercept form of the equation of the line, which is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
Answer
b
Answer for screen readers
The final answer is the y-intercept b
Steps to Solve
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Determine the slope (m) of the line given two points (x1, y1) and (x2, y2)
The slope formula is given by: $$ m = \frac{y2 - y1}{x2 - x1} $$
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Use the slope-intercept form of the line equation (y = mx + b)
Substitute one of the points (either ((x1, y1)) or ((x2, y2))) and the slope (m) into the line equation to solve for the y-intercept (b): $$ y1 = m \cdot x1 + b $$ Solve for b by isolating it on one side of the equation: $$ b = y1 - m \cdot x1 $$
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Write the final equation of the line
Now that you have the slope (m) and the y-intercept (b), you can write the equation of the line in the slope-intercept form: $$ y = mx + b $$ The value of b obtained in the previous step is the y-intercept.
The final answer is the y-intercept b
More Information
The y-intercept is the point where the line crosses the y-axis. It is often denoted by 'b' in the slope-intercept form of the line equation, y = mx + b.
Tips
A common mistake is to mix up the coordinates (x1, y1) and (x2, y2) when calculating the slope. Make sure to subtract the coordinates in the correct order to get the right value for the slope.
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