Answer:
y = 3x - 4
Step-by-step explanation:
The general structure of a line in slope-intercept form is:
y = mx + b
In this form, "m" is the slope and "b" is the y-intercept.
(Step 1)
Before you can determine this equation, you need to find the value of "m". Since you were given the value of two points, you can find this by using the point-slope form. The general structure of the point-slope equation is:
y₁ - y₂ = m(x₁ - x₂)
y₁ - y₂ = m(x₁ - x₂) <---- Point-slope equation
-1 - 8 = m(1 - 4) <---- Insert "x" and "y" values from table
-9 = m(1-4) <---- Simplify left side
-9 = -3m <---- Simplify inside parentheses
3 = m <---- Divide both sides by -3
(Step 2)
Now that you know "m", you can plug it and the "x" and "y" values of one point into the slope-intercept equation to find the value of "b".
y = mx + b <---- Slope-intercept equation
y = 3x + b <---- Plug 3 into "m"
-1 = 3(1) + b <---- Plug "x" and "y" values in
-1 = 3 + b <---- Multiply 3 and 1
-4 = b <---- Subtract 3 from both sides
(Step 3)
Now that you know that m = 3 and b = -4, you can substitute these values into the slope-intercept form to find your final answer. You can check your answer by plugging the "x" values from the table into the equation to verify that you get the correct "y" values.
y = 3x - 4
