Question

I need help with math homework

Answer 1

A. (1, 2) and (4, 3)

B. Slope (m) = ⅓

C. y - 2 = ⅓(x - 1)

D.
`y = (1)/(3)x + (5)/(3)`

E.
`-(1)/(3)x + y = (5)/(3)`

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) = (y_2 - y_1)/(x_2 - x_1) = (3 - 2)/(4 - 1) = (1)/(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

`y = (1)/(3)x + (5)/(3)`

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

`y = (1)/(3)x + (5)/(3)`

`-(1)/(3)x + y = (5)/(3)`