Question

Writing and Analyzing an Equation of a Line
You are given a line that has a slope of 4 and passes through the point (StartFraction 3 Over 8 EndFraction, one-half). Which statements about the equation of the line are true? Check all that apply.
The y-intercept is -1.
The slope-intercept equation is y = 4 x minus 1.
The point-slope equation is y minus StartFraction 3 Over 8 EndFraction = 4 (x minus one-half).
The Point (StartFraction 3 Over 8 EndFraction, one-half) corresponds to (x1, y1) in the point-slope form of the equation.

Answer 1

Answers: True, True, False, True.

Reasoning:
- Plug (3/8, 1/2) into y = 4x + b: 1/2 = 4(3/8) + b = 3/2 + b, so b = 1/2 − 3/2 = −1. So the y-intercept is −1 and y = 4x − 1 is the slope-intercept form.
- Point-slope form is y − y1 = m(x − x1). With (x1,y1) = (3/8, 1/2) it should be y − 1/2 = 4(x − 3/8), not y − 3/8 = 4(x − 1/2). Thus that statement is false.
- The given point does correspond to (x1,y1) in point-slope form.