Question

slope and y-intercept quick check
the function passes through the points (3, 7) and (12, 25).
write an equation that represents the y as a function of x
y = \boxed{}x + \boxed{}

Explanation:

Step1: Calculate the slope (m)

The slope formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1, y_1) = (3, 7)\) and \((x_2, y_2) = (12, 25)\). So, \(m=\frac{25 - 7}{12 - 3}=\frac{18}{9}=2\).

Step2: Find the y - intercept (b)

Use the point - slope form \(y - y_1=m(x - x_1)\) and substitute \(m = 2\), \(x_1 = 3\), \(y_1 = 7\). We get \(y-7 = 2(x - 3)\). Expand the right - hand side: \(y-7=2x-6\). Then, add 7 to both sides: \(y=2x + 1\). We can also use the slope - intercept form \(y=mx + b\) and substitute \(x = 3\), \(y = 7\), \(m = 2\) into it. So, \(7=2\times3 + b\), which simplifies to \(7 = 6 + b\). Subtract 6 from both sides: \(b = 1\).

Answer:

\(y = 2x+1\) (So the first blank is 2 and the second blank is 1)