Question

The equation of line R, shown below, can be

written in the form y = mx + c.
What are the values of m and c?
Give each of your answers as an integer or
as a fraction in its simplest form.
Y
6-
5-
4
3
2.
1
-5 -4 -3 -2 -1 0
-1.
--2-
--3/
Line R
1 2 3 4
5
X

PLEASE DO IT

Answer 1

• y = 5x -2
• m = 5
• c = -2

Explanation:

You want the values of m and c for the equation y = mx + c that describes the line on the graph.

M

The coefficient 'm' in the equation y = mx + c is the slope of the line. It is the ratio of the "rise" to the "run". The "rise" is the vertical distance from one point to another on the line. The "run" is the corresponding horizontal distance between the points.

For finding these values, it is convenient to locate points on the graph that cross grid line intersections. These are circled in the attachment.

The slope (m) of this line is ...

m = 5/1 = 5

C

The constant 'c' in the equation y = mx + c is the y-intercept of the line. It is the value of y when x=0. On the graph, it is the y-coordinate of the point where the line crosses the y-axis.

The line on this graph crosses the y-axis at y = -2.

The value of 'c' is -2.

The equation of the line is y = 5x -2.

__

Additional comment

You can find the values of "rise" and "run" from coordinates, or by counting grid squares on the graph. Often, counting the grid lines is easier.

Here, the "rise" is 3 -(-2) = 5, the difference of y-coordinates of the circled points.

The "run" is 1 -0 = 1, the difference of the corresponding x-coordinates of the circled points.

The slope is rise/run = 5/1 = 5.