Question

This is my last question help me please

Answer 1

y=2x-1 , y=x+2 , the solution of the system is (1,1)

Explanation:

Lines can be expressed in the form y=mx+b where m is the slope and b is the y-intercept.

m= rise/run

Looking at the blue line:

m =2/1 =2

The slope is 2 since you rise 2 squares and run to the right one square.

We see that the line crosses the y-axis at (0,-1) so the y-intercept is -1.

Putting it all together: y=2x-1

Looking at the red line:

m = -1 / 1 = -1

We see that the line crosses the y-axis at (0,2) so the y-intercept is 2.

Putting it all together: y=1x+2 or simply y=x+2

The solution to the system is the point that satisfies both equations. Rather than solving it algebraically, we can simply look at the graph and find a point that is on both lines, aka the intersection. In this case, the intersection is (1,1).

Answer 2

Line 1:
`y=-x+2`

Line 2:
`y=2x-1`

Explanation:

Line 1

Staring with line one, let's find the slope!

Between the two known points, the rise, or change in y, is 2, and the run, or change in x, is -2. The slope is the rise over the run, so:

`-(2)/(2) =-1`

The slope is negative 1! The line crosses the y-axis at
`y=2`, so 2 is the y-intercept. Using the slope-intercept formula, the equation is:

`y=-x+2`

Line 2

To find the slope of line 2, find the rise and the run between the two known points! The rise is 4, and the run is 2. Simplified, this is:

`(4)/(2) =2`

The slope is 2! The line crosses the y-axis at
`y=-1`, so -1 is the y-intercept. Using the slope-intercept formula, the equation is:

`y=2x-1`