Answer:
System of the equations will be y = x + 4 and y = x² + 2
Step-by-step explanation:
The system of equations comprises a parabola and a straight line.
We will form the equation of the line first.
Straight line given in the system passes through two points (2, 6) and (-1, 3).
Since standard for of a straight line is given by y = mx + c
where m = slope and c = y-intercept
So, Slope m = [tex]\frac{y-y'}{x-x'}[/tex]
m = [tex]\frac{6-3}{2+1}[/tex]
m = 1
And y-intercept c = 4
Therefore, equation of the line will be y = x + 4
For the equation of parabola.
Vertex form of the parabola is represented by,
y = (x - h)² + k
Where (h, k) is the vertex.
Vertex is given in the graph is (0, 2).
So the equation will be y = (x - 0)² + 2
y = x² + 2
Therefore, system of the equations will be y = x + 4 and y = x² + 2
