Slope-intercept form is:
y = mx + b
"m" is the slope, "b" is the y-intercept (the y value when x = 0)
You can find the slope either by using the slope formula and finding 2 points:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Or you can use this:
[tex]slope=\frac{rise}{run}[/tex]
Rise is the number of units you go up(+) or down(-)
Run is the number of units you go to the right
(I'm using rise/run) If you look at line P, from each point you go up 1 unit, and to the right 2 units. So your slope is 1/2. When x = 0, the y value is 6, so your y-intercept is 6.
Line P: [tex]y=\frac{1}{2}x + 6[/tex]
If you look at line Q, from each point you go down 4 units, and to the right 1 unit. So your slope is -4/1 or -4. When x = 0, the y value is -3, so your y-intercept is -3.
Line Q: [tex]y = -4x -3[/tex]
To find the solution to the system, you can find the point of intersection(the point where the lines meet). The point of intersection is (-2,5)
You can also do this by hand and set the equation of Line P and Q equal to each other to find x:
Line P: y = 1/2x + 6
Line Q: y = -4x - 3
1/2x + 6 = -4x - 3 Subtract 6 on both sides
1/2x = -4x - 9 Add 4x on both sides
1/2x + 4x = -9 Make the denominators the same
1/2x + 8/2x = -9
9/2x = -9 Multiply 2/9 on both sides to get x by itself
[tex](\frac{2}{9}) \frac{9}{2}x = -9(\frac{2}{9} )[/tex]
x = -2
Plug in -2 for x into either the equation of Line P or Line Q
y = -4x - 3
y = -4(-2) - 3
y = 8 - 3
y = 5
(-2,5)
