Answer:
y = 3x - 11
Step-by-step explanation:
To find out linear equation, you must first determine what the rate of change (slope) is, given the table of values.
Choose two set of points from the table.
Let (x1, y1) = (3, -2)
(x2, y2) = (5, 4)
Use the slope formula, and substitute the given values:
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{4 - (-2)}{5 - 3} = \frac{6}{2} = 3[/tex]
Therefore, the slope of the equation is 3.
Next, you need to determine the y-intercept of the line. The y-intercept is the point in the graph where it crosses the y-axis; it is also the value of y when x = 0.
Using the point-slope form: y - y1 = m(x - x1)
where m = slope
and (x1, y1) is the set of ordered pairs.
Plug in the value of the slope, and one of the given ordered pairs on your table, (3, -2) into the point-slope equation:
y - y1 = m(x - x1)
y - (-2) = 3(x - 3)
Distribute 3 into (x - 3):
y + 2 = 3x - 9
Subtract 2 from both sides to isolate y:
y + 2 - 2 = 3x - 9 - 2
y = 3x - 11 ←←← This is the equation of the line where the slope = 3, and the y-coordinate of the y-intercept is -11.
Please mark my answers as the Brainliest if my explanations were helpful :)
