How to graph Y=5/2X-4

2 Answers

ishpiro's profile pic

ishpiro | College Teacher | (Level 1) Educator

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This is the equation of a line in slope-intercept form, or, in general,

y = mx + b.

The slope is m = 5/2 and y-intercept is (0, b) is (0, -4).

Since the equation is given in slope-intercept form, it is convenient to graph it using the slope and the y-intercept.

First, plot y-intercept (0, -4). This is a point where the line intersects y-axis. To graph it, start at the origin and go 4 units down y-axis.

Next, use the fact that we know the slope, which indicates the direction in which the line is going. The slope can be described as rise/run, or vertical change divided by horizontal change. This means, if the slope is 5/2, when x changes by 2 units, y will change by 5 units.

To find another point on the line, count 2 units to the right (positive direction of x) and 5 units up (positive direction of y). This will bring you to the point 

(0 + 2, -4 + 5) = (2, 1)

The two points (0, -4) and (2, 1) are enough to draw a unique line, but if you want to get more points, you can repeat the process: starting with the point (2, 1), count 2 units to the right and 5 units up. This will bring you to the point

(2 + 2, 1 + 5) = (4, 6)

Alternatively, or in addition, start again with (0, -4) and go in the opposite direction: 2 units to the left and 5 units down. This will bring you to the point

(0 -2, -4 -5) = (-2, -9).

Drawing straight line through these points will result in the graph shown below:


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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The equation that you have to draw a graph of is y = (5/2)*x - 4.

This is the equation of a straight line in slope-intercept form y = mx + c. Here, the slope of the line us 5/2 and the y-intercept is -4.

A straight line is uniquely defined if two points that lie on the line are known.

Consider the points with x-coordinate equal to 0 and the y-coordinate equal to 0.

When x-coordinate is 0, y = 0 - 4 = -4 and when the y-coordinate is 0, 0 = 2.5*x - 4

x = 4/2.5

x = 1.6

The points (1.6, 0) and (0, -4) lie on the given line.

The graph of the line is a straight line that passes through these 2 points.