Question

Can someone answer these two questions I submitted a photo of them it’s worth 50 points

Answer 1

Explanation:

1). Let the equation of the line is,

y = mx + b

Here, m = slope of the line

b = y-intercept

Slope of a line passing through two points,

m =
`(y_2-y_1)/(x_2-x_1)`

We take two points from the table given (-3, -19) and (0, -1)

m =
`(-19+1)/(-3-0)`

m = 6

y - intercept 'b' = -1 [For x = 0]

Therefore, equation of the line will be,

y = 6x - 1

2). Equation of a line passing through a point (x', y') is,

y - y' = m(x - x')

Slope of the line passing through two points
`(x_1,y_1)` and
`(x_2,y_2)` is,

m =
`(y_2-y_1)/(x_2-x_1)`

We take two points from the given table as (2, 12) and (3, 18).

Slope of the line passing through these points will be

m =
`(18-12)/(3-2)` = 6

Equation of the line passing through (2, 12) will be,

y - 12 = 6(x - 2)

y = 6x - 12 + 12

y = 6x

By using a graphing tool we can graph these lines representing the tables.