Graph 2x-5y=22 and x + 5y=-4 on the same axis

Question

Graph both equasions on the same set of axis then reading the solution of the graph.

2x-5y=22

x + 5y=-4

Answer 1

The equations are 2x - 5y = 22 and  x + 5y = - 4

• First line 2x - 5y = 22

Write the equation in slope-intercept form y = mx + b, where m is slope and b is y -intercept.

y = 2x/5 - 22/5

y = 2x/5 - 4.4

Compare the equation with slope-intercept form y = mx + b.

slope = 2/5 and y -intercept is - 4.4.

y -intercept is - 4.4, so the line crosses the y - axis at (0, - 4.4)

Using slope find the next point.

Slope = rise/run = 2/5

Start at point (0, - 4.4), move 2 units up and 5 units right, then plot the point (5, - 2.4).

Draw a line through these points.

• Second line x + 5y = - 4

y = - x/5 - 4/5

y = - x/5 - 0.8

Compare the equation with slope-intercept form y = mx + b.

slope = - 1/5 and y-intercept is - 0.8.

y -intercept is - 0.8. so the line crosses the y -axis at (0, - 0.8)

Using slope find the next point.

Slope = rise/run = - 1/5

Start at point (0, - 0.8), move 1 unit down and 5 unit right, then plot the point (5, - 1.8).

Draw a line through these points.

Graph

From the graph we can observe the two lines are intersecting at (6, -2).

Solution is x = 6, y = -2.