I need help with math homework
1 answer:
Answer:
A. (1, 2) and (4, 3)
B. Slope (m) = ⅓
C. y - 2 = ⅓(x - 1)
D.
E.
Step-by-step explanation:
A. Two points on the line from the graph are: (1, 2) and (4, 3)
B. The slope can be calculated using two points, (1, 2) and (4, 3):
Slope (m) = ⅓
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, 2), and m = ⅓ into the point-slope equation, y - b = m(x - a).
Thus:
y - 2 = ⅓(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 - 2 = ⅓(x - 1)
3(y - 2) = x - 1
3y - 6 = x - 1
3y = x - 1 + 6
3y = x + 5
E. Convert the equation in (D) to standard form:
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Answer:
= (x -1)(x + 1)(x - 4)(x + 4)
Step-by-step explanation:
At first, let us find the first two factors of
∵ The sign of the last term is positive
∴ The middle signs of the two factors are the same
∵ The sign of the middle term is negative
∴ The middle signs of the two factors are negative
∵ = x² × x² ⇒ first terms of the two factors
∵ 16 = -1 × -16 ⇒ second terms of the two factors
∵ x²(-1) + x²(-16) = -x² + -16x² = -17x² ⇒ the value of the middle term
∴ (x² - 1) and (x² - 16) are the factors of
Now let us factorize each factor
→ The factors of the binomial a² - b² (difference of two squares) are
(a - b) and (a + b)
∵ x² - 1 is the difference of two squares
∴ Its factors are (x - 1) and (x + 1)
∵ x² - 16 is the difference of two squares
∴ Its factors are (x - 4) and (x + 4)
∵ (x -1), (x + 1), (x - 4), and (x + 4) are the factors of (x² - 1) and (x² - 16)
∵ (x² - 1) and (x² - 16) are the factors of
∴ (x -1), (x + 1), (x - 4), and (x + 4) are the factors of
∴ = (x -1)(x + 1)(x - 4)(x + 4)