Question

module 11 (linear equations) assignment
score: 12/20 answered: 12/20
question 13
find the equation of the line, in slope - intercept form, i.e., $y = mx + b$, through the points $(-2,7)$ and $(1,1)$.
$y = $
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Explanation:

Step1: Calculate the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((-2, 7)\) and \((1, 1)\), we have \(x_1=-2\), \(y_1 = 7\), \(x_2=1\), \(y_2 = 1\). So \(m=\frac{1 - 7}{1 - (-2)}=\frac{-6}{3}=-2\).

Step2: Find the y-intercept (b)

We use the slope - intercept form \(y=mx + b\) and one of the points, say \((1, 1)\) with \(m=-2\). Substitute \(x = 1\), \(y = 1\) and \(m=-2\) into the equation: \(1=-2(1)+b\). Solve for \(b\): \(1=-2 + b\), then \(b=1 + 2=3\).

Step3: Write the equation

Now that we have \(m=-2\) and \(b = 3\), the slope - intercept form of the line is \(y=-2x+3\).

Answer:

\(y=-2x + 3\)