Question

write an equation of the line in point - slope form that passes through the given points in the table. then write the equation in slope - intercept form.
an equation of the line in point - slope form is \\(\square\\).
(simplify your answer. type an equation. type your answer in point - slope form. use integers or fractions for any numbers in the equation)
\\(\

$$\begin{array}{|c|c|c|c|c|c|}\\hline x&25&30&35&40&45\\\\\\hline y&240&275&310&345&380\\\\\\hline\\end{array}$$

\\)

Explanation:

Step1: Find the slope

We use two points from the table, say \((25, 240)\) and \((30, 275)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). So \(m=\frac{275 - 240}{30 - 25}=\frac{35}{5} = 7\).

Step2: Write point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\). We can use the point \((25, 240)\) and \(m = 7\). Substituting these values, we get \(y - 240=7(x - 25)\).

Answer:

\(y - 240 = 7(x - 25)\) (or using other points from the table, e.g., if we use \((30,275)\), the equation would be \(y - 275=7(x - 30)\), etc. The form \(y - y_1=m(x - x_1)\) with \(m = 7\) and a point \((x_1,y_1)\) from the table is correct)