Question

write the equation of this line in slope - intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Find the y - intercept (\(b\))

The y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at \((0,2)\), so \(b = 2\).

Step3: Calculate the slope (\(m\))

The slope \(m\) is calculated using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\) for two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line. We can use the points \((0,2)\) and \((- 1,0)\) (we can see that when \(x=-1\), \(y = 0\) from the graph).
Substitute \(x_1 = 0,y_1 = 2,x_2=-1,y_2 = 0\) into the slope formula:
\(m=\frac{0 - 2}{-1-0}=\frac{-2}{-1}=2\)

Step4: Write the equation

Substitute \(m = 2\) and \(b = 2\) into the slope - intercept form \(y=mx + b\). We get \(y = 2x+2\).

Answer:

\(y = 2x + 2\)