QQuestionMathematics
QuestionMathematics
What is the y-intercept of the line that passes through the two points with coordinates (5, - 2) and (1, 3)?
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Answer
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Step 1:I'll solve this step-by-step using the point-slope form and slope formula:
Step 2:: Calculate the slope of the line
m = \frac{3 - (-2)}{1 - 5} = \frac{5}{-4} = -\frac{5}{4}
• Plugging in the points (5, - 2) and (1, 3):
Step 3:: Use point-slope form
• Substituting: $$y - (-2) = -\frac{5}{4}(x - 5)
• Choose either point, let's use (5, - 2)
Step 4:: Simplify the equation
• $$y + 2 = -\frac{5}{4}(x - 5)
• y + 2 = -\frac{5}{4}x + \frac{25}{4}
Step 5:: Rearrange to slope-intercept form
• $$y = -\frac{5}{4}x + \frac{17}{4}
• y = -\frac{5}{4}x + \frac{25}{4} - \frac{8}{4}
Step 6:: Identify y-intercept
• The y-intercept is the $$y$$ value when $$x = 0
• Y-intercept = \frac{17}{4}
Final Answer
\frac{17}{4} or 4.25
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