## Compassionate one year ago find the point where a line with slope 1 and y-intercept (0, 4) intercepts a line through P(4, 8) and Q(-2, -1). What is the point of intersection

1. Nnesha

the point where a line with slope 1 and y-intercept (0, 4) y=mx+b slope intercept form where m is slope and b is y-intercept now plugin m and b value

2. Compassionate

I get that, but why do I need to know points P and Q. Why are they even in the problem.

3. Nnesha

you have to find 2nd equation through those (p and q) points

4. Compassionate

y = mx + b y = 1x + 4

5. Nnesha

then we can graph both equations to find out the intersection point |dw:1443817214823:dw|

6. Nnesha

right can you write the equation that passes through p and q points ??

7. Compassionate

P(4, 8) and Q(-2, -1) y = 1x + 4 8 = 4 + 4 = 8 -1 = 1(-2) + 4 -1 = 2? I don't know

8. Nnesha

hmm nope alright let's write the equation first we need to find the slope $\huge\rm m=\frac{ y_2 -y_1 }{ x_2 -x_1 }$now substitute x's and y's values from this order pair (4,8)(-2,-1)

9. Nnesha

$\rm (\color{ReD}{4},\color{blue}{8})(\color{orange}{-2},\color{green}{-1})$ $\rm (\color{ReD}{x_1},\color{blue}{y_1})(\color{orange}{x_2},\color{green}{y_2})$

10. Compassionate

I'm just having trouble understanding what they're even meaning. What point of intesection am I trying to find?

11. Compassionate

(4,8)(-2,-1) -1 - 8 -2 - 4 -9 -6 1.5

12. Nnesha

intersect point of equation y=1x+ 4 and PQ points it's same as system of equations questions where we have the 2 equations and we should find x and y values by using elimination/addition graphing matrices method

13. Nnesha

for this question the problem is they want us to find 2nd equation from PQ points

14. Nnesha

1.5 is right but better to keep it in fraction $\huge\rm y=\frac{ 3 }{ 2 }x+b$ replaced m with slope which is 3/2 now we can pick one of the point to find y-intercept let's use point Q (-2,-1) substitute x and y for (-2,-1) solve for b $-1= \frac{ 3 }{ 2 }(-2)+b$ b= ??

15. Nnesha

well pretty sure you know how to solve for b $\rm -1=\frac{ 3 }{ \cancel{2} }(-\cancel{2})+b$ $\rm -1=-3+b$ move to the left side $\rm -1+3=b$ b=2 so 2nd equation (PQ) would be y=3/2x +2 first equation $\large\rm y=1x+4$ 2nd equation $\large\rm y=\frac{ 3 }{ 2 }x+2$

16. Nnesha

now we have two equations there are 4 ways to solve for x and y (in other words to find intersection point ) substitution graphing elimination/addition matrices ~~~ graphing one is easy if both equations are in standard form then u should use elimination and if one of the equations solved for either x or y variable then you can use substitution

17. Nnesha

for this question substitution would be easy :=)