Question

I need help with math homework

Answer 1

Answer:

A. (0, 1) and (2, -2)

B. Slope (m) = -³/2

C. y + 2 = -³/2(x - 2)

D. $y = -\frac{3}{2}x + 1$

E. $\frac{3}{2}x + y = 1$

Step-by-step explanation:

A. Two points on the line from the graph are: (0, 1) and (2, -2)

B. The slope can be calculated using two points, (0, 1) and (2, -2):

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 1}{2 - 0} = \frac{-3}{2} = -\frac{3}{2}$

Slope (m) = -³/2

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) = (2, -2), and m = -³/2 into the point-slope equation, y - b = m(x - a).

Thus:

y - (-2) = -³/2(x - 2)

y + 2 = -³/2(x - 2)

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 = -³/2(x - 2)

2(y + 2) = -3(x - 2)

2y + 4 = -3x + 6

2y = -3x + 6 - 4

2y = -3x + 2

y = -3x/2 + 2/2

$y = -\frac{3}{2}x + 1$

E. Convert the equation in (D) to standard form:

$y = -\frac{3}{2}x + 1$

$\frac{3}{2}x + y = 1$