Question

find the equation of this line. simplify your answer completely. the graph shows a line with points plotted. the equation is in the form y = ?x +...

Explanation:

Step1: Identify two points on the line

We can see from the graph that the line passes through \((0, 3)\) (the y - intercept) and \((1, 4)\) (since when \(x = 1\), \(y = 4\)).

Step2: Calculate the slope \(m\)

The formula for slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((0,3)\) and \((1,4)\), we have \(x_1 = 0,y_1 = 3,x_2=1,y_2 = 4\). Then \(m=\frac{4 - 3}{1 - 0}=\frac{1}{1}=1\).

Answer:

The slope of the line is \(1\), so the equation of the line is \(y = 1x+3\) (and the value in the box is \(1\)).