Math  /  Algebra

QuestionA line passes through the point (8,3)(8,-3) and has a slope of 54-\frac{5}{4}. Write an equation in slope-intercept form for this line. \square

Studdy Solution
Simplify and convert to slope-intercept form y=mx+by = mx + b.
First, simplify the left side:
y+3=54(x8) y + 3 = -\frac{5}{4}(x - 8)
Distribute the slope on the right side:
y+3=54x+54×8 y + 3 = -\frac{5}{4}x + \frac{5}{4} \times 8
y+3=54x+10 y + 3 = -\frac{5}{4}x + 10
Subtract 3 from both sides to solve for yy:
y=54x+103 y = -\frac{5}{4}x + 10 - 3
y=54x+7 y = -\frac{5}{4}x + 7
The equation of the line in slope-intercept form is:
y=54x+7 y = -\frac{5}{4}x + 7

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