Write an equation in slope-intercept form for a line that passes through the given pair of points. (7, 2) (1, 0)

Accepted Solution

Answer:[tex]y=\frac{1}{3}x-\frac{1}{3}[/tex]Step-by-step explanation:THe slope intercept form of a line is y = mx + bWhere, m is the slope with formula  [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]andb is the y-intercept (the point where the line cuts the y-axis)x_1 and y_1 is the first pair of pointsx_2, y_2 is the second pair of pointsLet's find m first by plugging in the points:[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{0-2}{1-7}\\m=\frac{-2}{-6}\\m=\frac{1}{3}[/tex]Now we have y = 1/3x+b. We can plug in any point (let's use (1,0)) and find b:[tex]y=\frac{1}{3}x+b\\0=\frac{1}{3}(1)+b\\0=\frac{1}{3}+b\\b=-\frac{1}{3}[/tex]THus, the equation of the line is  [tex]y=\frac{1}{3}x-\frac{1}{3}[/tex]