Question

find the slope and y-intercept.
slope:
y-intercept:

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((0, 2)\) (where \(x = 0\), this is the y - intercept point) and \((1, 5)\) (we can find another point by moving 1 unit in the x - direction and 3 units in the y - direction from \((0,2)\), or we can use the grid to find another point. Let's confirm with \((0,2)\) and \((1,5)\)). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Calculate the slope

Using the points \((x_1,y_1)=(0,2)\) and \((x_2,y_2)=(1,5)\), we substitute into the slope formula: \(m=\frac{5 - 2}{1 - 0}=\frac{3}{1}=3\).

Step3: Find the y - intercept

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,2)\), we can see that when \(x = 0\), \(y=2\). So the y - intercept is 2.

Answer:

slope: \(3\)
y - intercept: \(2\)