Question

write the equation of the line that is graphed. use slope-intercept form, ( y = mx + b ).
watch this video if you need help completing this question!!!
(1 point)
the y-intercept of the line is 2
the slope of the line is
( y = square x + 2 )

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, 2)\) (the y - intercept) and another point, say \((4, 3)\) (by counting the grid squares: moving 4 units to the right and 1 unit up from the y - intercept).

Step2: Calculate the slope (\(m\))

The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(0, 2)\) and \((x_2,y_2)=(4, 3)\), we have \(m=\frac{3 - 2}{4 - 0}=\frac{1}{4}\).

Step3: Write the equation in slope - intercept form

The slope - intercept form is \(y = mx + b\), where \(b = 2\) (the y - intercept) and \(m=\frac{1}{4}\). So the equation is \(y=\frac{1}{4}x + 2\).

Answer:

The slope of the line is \(\frac{1}{4}\), and the equation of the line is \(y=\frac{1}{4}x + 2\). So the slope box should be filled with \(\frac{1}{4}\) and the \(y=\square x + 2\) box should be filled with \(\frac{1}{4}\).