3. The number of hours you study for an exam impacts your grade. What is a reasonable value of the range?
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Answer:
A. (-5, 0) and (1, -3)
B. Slope (m) = -½
C. y + 3 = -½(x - 1)
D. y = -½x - ⁵/2
E. ½x + y = ⁵/2
Step-by-step explanation:
A. Two points on the line from the graph are: (-5, 0) and (1, -3)
B. The slope can be calculated using two points,(-5, 0) and (1, -3):
Slope (m) = -½
C. Equation in point-slope form is represented as y - b = m(x - a). Where,
(a, b) = any point on the graph.
m = slope.
Substitute (a, b) = (1, -3), and m = -½ into the point-slope equation, y - b = m(x - a).
Thus:
y - (-3) = -½(x - 1)
y + 3 = -½(x - 1)
D. Equation in slope-intercept form, can be written as y = mx + b.
Thus, using the equation in (C), rewrite to get the equation in slope-intercept form.
y + 3 = -½(x - 1)
2(y + 3) = -1(x - 1)
2y + 6 = -x + 1
2y = -x + 1 - 6
2y = -x - 5
y = -x/2 - ⁵/2
y = -½x - ⁵/2
E. Convert the equation in (D) to standard form:
y = -½x - ⁵/2
½x + y = ⁵/2