Question

the table shows several points that lie along a line when plotted on a coordinate plane.

x	-2	-1	3	5
y	-5	-2	10	16

write an equation of the line defined by these points.
type your answer in the box.

Explanation:

Step1: Find the slope (m)

Use two points, e.g., \((-2, -5)\) and \((-1, -2)\). The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
\(m=\frac{-2 - (-5)}{-1 - (-2)}=\frac{3}{1}=3\)

Step2: Use point - slope form to find the equation

Point - slope form is \(y - y_1=m(x - x_1)\). Let's use the point \((-2, -5)\) and \(m = 3\).
\(y-(-5)=3(x - (-2))\)
\(y + 5=3(x + 2)\)
Expand the right - hand side: \(y+5 = 3x+6\)
Subtract 5 from both sides: \(y=3x + 1\)

We can check with another point, say \((3,10)\). Substitute \(x = 3\) into \(y = 3x+1\), we get \(y=3\times3 + 1=10\), which matches the table. Also, for \(x = 5\), \(y=3\times5+1 = 16\), which also matches.

Answer:

\(y = 3x+1\)