Answer:
y = 4x - 9
Step-by-step explanation:
The points on the graph we can see clearly are (1, -5) and (2, -1).
The equation of the line is in the form slope-intercept, where the general formula is y = mx + b.
We need to find "m", the slope of the line; and "b", the y-intercept.
Use the two points we found in the formula for calculating slope [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
Choose which is point 1 and point 2:
Point 1 (1, -5) x₁ = 1 y₁ = -5
Point 2 (2, -1) x₂ = 2 y₂ = -1
Substitute x₁, x₂, y₁, and y₂
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{-1-(-5)}{2-1}[/tex] Solve in the numerator and denominator
[tex]m=\frac{4}{1}[/tex] Simplify the fraction
[tex]m=4[/tex] Slope of the line
Find "b":
Substitute a point's "x" and "y" coordinates, and the slope, "m", into the general formula for slope-intercept.
I will use point 2:
x = 2; y = -1; m = 4
y = mx + b
-1 = (4)(2) + b Multiply
-1 = 8 + b Start isolating "b"
-1 - 8 = 8 - 8 + b Subtract 8 from both sides
-1 - 8 = b "b" is isolated
b = -9 Answer for "b", y-intercept.
The variable should be on the left side for standard formatting.
Take the general formula: y = mx + b
Replace "m" and "b" with the values we found.
y = 4x - 9
