Question

Can I get some help?​

Answer 1

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 $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$.

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

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{-1-(-5)}{2-1}$       Solve in the numerator and denominator

$m=\frac{4}{1}$        Simplify the fraction

$m=4$           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