Question

1. write an equation in slope - intercept form of the line that passes through (-3, 5) and (-2, 6). equation: y = \square

Explanation:

Step1: Find the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Given points \((-3, 5)\) and \((-2, 6)\), we have \(x_1=-3\), \(y_1 = 5\), \(x_2=-2\), \(y_2 = 6\). So \(m=\frac{6 - 5}{-2-(-3)}=\frac{1}{1}=1\).

Step2: Find the y-intercept (b)

Use the slope-intercept form \(y = mx + b\) and one of the points, say \((-3, 5)\) with \(m = 1\). Substitute into the equation: \(5=1\times(-3)+b\). Solve for \(b\): \(5=-3 + b\), so \(b=5 + 3=8\).

Step3: Write the equation

Now that \(m = 1\) and \(b = 8\), the slope - intercept form is \(y=mx + b\), so \(y=1\times x+8\) or \(y=x + 8\).

Answer:

\(y=x + 8\)