Question

write an equation in slope - intercept form of the line that passes through the given points.

x	-2	0	2	4
y	2	1	0	-1

y = \square

Explanation:

Step1: Find the slope (m)

We use two points, say \((-2, 2)\) and \((0, 1)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting the values: \(m=\frac{1 - 2}{0 - (-2)}=\frac{-1}{2}=-\frac{1}{2}\).

Step2: Find the y-intercept (b)

The slope - intercept form is \(y = mx + b\). We know \(m = -\frac{1}{2}\), and we can use the point \((0, 1)\) (when \(x = 0\), \(y=b\)). So \(b = 1\).

Step3: Write the equation

Substitute \(m=-\frac{1}{2}\) and \(b = 1\) into \(y=mx + b\). We get \(y=-\frac{1}{2}x + 1\).

Answer:

\(y = -\frac{1}{2}x + 1\)