Question
PREPARATION SHEET, MIDTERM 1 1. Write the equation of a line through each indicated point with the indicated slope. Write the final answer in the form \( y=m x+b \). (A) \( m=-\frac{2}{3} ;(-3,2) \) (B) \( m=0 ;(3,3) \)
Ask by Deleon King. in Kazakhstan
Feb 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
A) \( y = -\frac{2}{3}x \)
B) \( y = 3 \)
Solution
Рассмотрим каждую задачу по отдельности.
A) Дано: угол наклона m = –2/3 и точка (–3, 2).
Используем уравнение прямой в точке:
y – y₁ = m (x – x₁).
Подставляем значения:
y – 2 = –(2/3)(x – (–3)) = –(2/3)(x + 3).
Раскрываем скобки:
y – 2 = –(2/3)x – 2.
Прибавляем 2 к обеим частям:
y = –(2/3)x – 2 + 2,
y = –(2/3)x.
Итак, уравнение прямой в форме y = mx + b:
y = –(2/3)x.
B) Дано: угол наклона m = 0 и точка (3, 3).
Прямая с угловым коэффициентом 0 — горизонтальная прямая. Ее уравнение:
y = b.
Подставляем координату точки:
3 = b,
b = 3.
Таким образом, уравнение прямой:
y = 3.
Ответ:
A) y = –(2/3)x
B) y = 3.
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Simplify this solution The Deep Dive
To find the equation of a line in the form \( y = mx + b \), you can use the point-slope form of the equation and then convert it to the desired format. For part (A), start with the point \((-3, 2)\) and slope \( m = -\frac{2}{3}\). The point-slope form is \( y - y_1 = m(x - x_1) \), which gives us \( y - 2 = -\frac{2}{3}(x + 3) \). Expanding this leads to the final equation \( y = -\frac{2}{3}x - 2 \). For part (B), with a slope of \( m = 0 \), the line is horizontal. This means \( y \) will be the same value as the y-coordinate of the point \((3, 3)\). Therefore, the final equation is simply \( y = 3 \).
