Question

assignment 2.2 linear equations in one variable
score: 11/13 answered: 12/13 progress saved done
question 13
if a line has an x-intercept at x = 10 and a y-intercept at y = 2, find its equation in the form y = mx + b.
y =
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Explanation:

Step1: Identify intercept points

The x - intercept is at \(x = 10\), so the point is \((10,0)\). The y - intercept is at \(y=2\), so the point is \((0,2)\). In the slope - intercept form \(y = mx + b\), \(b\) is the y - intercept. So \(b = 2\).

Step2: Calculate the slope \(m\)

The formula for the slope \(m\) 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 \((10,0)\) (where \(x_1 = 10,y_1 = 0\)) and \((0,2)\) (where \(x_2=0,y_2 = 2\)):
\(m=\frac{0 - 2}{10-0}=\frac{- 2}{10}=-\frac{1}{5}\)

Step3: Write the equation

Now that we have \(m=-\frac{1}{5}\) and \(b = 2\), substitute these values into the slope - intercept form \(y=mx + b\).
So the equation is \(y=-\frac{1}{5}x + 2\)

Answer:

\(y = -\frac{1}{5}x+2\)