Write an equation in slope-intercept form for the line that satisfies the following condition,
passes through (13,9) and (30, 26)

Equation is y = 15/17 x - 42/17

Step-by-step explanation:

Find slope of the line. m = (y2 - y1)/(x2 - x1) Here, x1 = 13, x2 = 30, y1 = 9, y2 = 26

⇒ m = (26 - 9)/(30 - 13) = 15/17

Form the equation with slope m=15/17

⇒ y = 15/17 x + b   (1)

Find the y-intercept, b. Substitute the values of x = 13 and y = 9 in the eq(1) to find b.

⇒ 9 = 15/17 × 13 + b = 195/17 + b

⇒ b = 9 - 195/17 = 153 - 195/17 = -42/17

Substitute the values of m and b to form the equation

⇒ y = 15/17 x - 42/17