Question

the graph of a linear function passes through the points (3,7) and (4,10). write an equation for the function.

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points (3, 7) and (4, 10), we have $x_1 = 3$, $y_1 = 7$, $x_2 = 4$, $y_2 = 10$. So $m = \frac{10 - 7}{4 - 3} = \frac{3}{1} = 3$.

Step2: Use point - slope form

The point - slope form of a linear equation is $y - y_1 = m(x - x_1)$. We can use the point (3, 7) and $m = 3$. Substituting these values in, we get $y - 7 = 3(x - 3)$.

Step3: Simplify to slope - intercept form

Expand the right - hand side: $y - 7 = 3x - 9$. Then add 7 to both sides: $y = 3x - 9 + 7$, which simplifies to $y = 3x - 2$.

Answer:

$y = 3x - 2$