Respuesta :
Let's make an equation that represents the linear function passing through points (1,2) and (4,1) by Slope-Intercept Form.
[tex]\text{ y = mx+b}[/tex]In making an equation in this form, we must first determine the value of the slope (m) and the y-intercept (b) of the line.
For determining the value of the slope, we use this formula,
[tex]\text{ m = }\frac{y_2-y_1\text{ }}{x_2-x_1}[/tex]Let's substitute (x1,y1) = (1,2) and (x2,y2) = (4,1), we get,
[tex]\text{ m = }\frac{1\text{ - 2}}{4\text{ -1}}\text{ = }\frac{-1}{3}\text{ = -}\frac{1}{3}[/tex]Let's now compute for the value of the y-intercept (b),
m = -1/3 and (x1,y1) = (1,2)
[tex]\text{ y = mx + b}[/tex][tex]\text{ (2) = (-}\frac{1}{3})(1)\text{ + b}[/tex][tex]\text{ 2 = -}\frac{1}{3}\text{ + b }\rightarrow\text{ b = 2 + }\frac{1}{3}\text{ = }\frac{6\text{ + 1}}{3}[/tex][tex]\text{ b = }\frac{7}{3}[/tex]Let's now make the equation substituting the value of m and b.
m = -1/3 and b = 7/3
[tex]\text{ y = (}\frac{-1}{3})x\text{ + }\frac{7}{3}[/tex][tex]\text{ y = -}\frac{1}{3}x\text{ + }\frac{7}{3}[/tex]