Question

Consider the graph below
Find the y-intercept and slope of the line. Fill in the blanks in the statement.

The y-intercept of the line is ______, and the slope of the line is ______.

Answer 1

Answer:

Slope: -1/2

y-intercept: (0, 6)

Step-by-step explanation:

The y-intercept is where the line intersects the y-axis which is (0, 6)

To find the slope, we can use the formula  $\frac{x2 - x1}{y2 - y1}$ where each (x, y) is a different coordinate of a point on the line.

Plug any coordinates into the formula (ex. (0, 6) and (3, 0))

x1 = 0

x2 = 3

y1 = 6

y2 = 0

The order for the variables does not matter as long as you keep the coordinates together in the formula (ex. x2 and y2 can be x1 and y1).

Solve the equation

$\frac{3 - 0}{0 - 6}$

$-\frac{3}{6}$  

Simplifies to -1/2

Let me know if you have any questions!

Answer 2

Answer: 6 and -2

Step-by-step explanation:

Finding the y-intercept of the graph is easy because the y-intercept is the point at which a graph crosses the y-axis. It is represented by the coordinates (0,y), where y is the value of the y-intercept. This means that we can find it without even calculating but by just looking at the graph.

From the graph, we see that the line intersects the y-axis at (0,6) so the y-intercept is 6.

The slope, however, is harder to find. It is calculated by taking the difference in the y-values of two points on the line and dividing it by the difference in the x-values of those same two points. Remember, this can be any two points that the graph pass through.

So we can find the slope by calculating (6 - 0) ÷ (0 - 3) = -2 so the slope is -2