Answer:
Step-by-step 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 = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We take two points from the table given (-3, -19) and (0, -1)
m = [tex]\frac{-19+1}{-3-0}[/tex]
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 [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
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 = [tex]\frac{18-12}{3-2}[/tex] = 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.
