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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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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