Question

name date 12-16-25 page 2
write a linear equation from two points
keep going! in each problem, youve been given a pair of points that lie on a line. use the points to
write the equation of the line in slope - intercept form.

1. points: (4, -4) and (10, 8)

equation:

1. points: (-2, 9) and (2, -7)

equation:

Explanation:

Problem 3:

Step1: Find the slope ($m$)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For points \((4, - 4)\) and \((10,8)\), \(x_1 = 4,y_1=-4,x_2 = 10,y_2 = 8\). So \(m=\frac{8-(-4)}{10 - 4}=\frac{12}{6}=2\).

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

Use the slope - intercept form \(y=mx + b\) and one of the points, say \((4,-4)\) with \(m = 2\). Substitute \(x = 4,y=-4,m = 2\) into \(y=mx + b\): \(-4=2\times4 + b\). Simplify: \(-4 = 8 + b\). Subtract 8 from both sides: \(b=-4 - 8=-12\).

Step3: Write the equation

Using \(m = 2\) and \(b=-12\) in \(y=mx + b\), the equation is \(y = 2x-12\).

Problem 4:

Step1: Find the slope ($m$)

For points \((-2,9)\) and \((2,-7)\), using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \(x_1=-2,y_1 = 9,x_2=2,y_2=-7\). So \(m=\frac{-7 - 9}{2-(-2)}=\frac{-16}{4}=-4\).

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

Use the slope - intercept form \(y=mx + b\) and one of the points, say \((2,-7)\) with \(m=-4\). Substitute \(x = 2,y=-7,m=-4\) into \(y=mx + b\): \(-7=-4\times2 + b\). Simplify: \(-7=-8 + b\). Add 8 to both sides: \(b=-7 + 8 = 1\).

Step3: Write the equation

Using \(m=-4\) and \(b = 1\) in \(y=mx + b\), the equation is \(y=-4x + 1\).

Answer:

(Problem 3):
\(y = 2x-12\)