x+y=8 and x-3y=-4 solved using graphing

Question

Solve using graphing.

Answer 1

First line x + y = 8

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

The equation is x + y  = 8

Subtract x from each side.

y  = - x + 8

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

slope = -1 and y -intercept is 8.

y -intercept is 8, so the line crosses the y -axis at (0, 8)

Using slope find the next point.

Slope = rise/run = -1

Start at point (0, 8), move 1 unit down and 1 unit right, then plot the point (1, 7).

Draw a line through these points.

Now  the second line x - 3y  = -4

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

The equation is x - 3y  = -4

Subtract x from each side.

-3y  = - x - 4

Divide each side by negitive 3.

y  =  x /3 + 4/3

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

slope = 1/3 and y -intercept is 1.33.

y -intercept is 1.33, so the line crosses the y -axis at (0, 1.33)

Using slope find the next point.

Slope = rise/run = 1/3

Start at point (0, 1.33), move 1 unit up and 3 units right, then plot the point (3, 2.33).

Draw a line through these points.

Graph :

From the graph lines are intersecting at (5,3).

Solution x = 5 and y = 3.