Question

danna graphed the first of two equations in a system of linear equations. if the graph of the second equation in the system passes through the points (-2,20) and (6,4), which statement is true? select two correct answers. the system has an infinite number of solutions. the only solution to the system is (8,6). the equation of the second line is y=-2x + 16. the only solution to the system is (4,8). the system has no solution. the equation of the second line is y=-2x+24.

Explanation:

Step1: Find the slope of the second - line

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given points $(-2,20)$ and $(6,4)$, we have $m=\frac{4 - 20}{6-(-2)}=\frac{-16}{8}=- 2$.

Step2: Find the y - intercept of the second - line

Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(6,4)$ and $m=-2$, we get $y - 4=-2(x - 6)$. Expand to $y-4=-2x + 12$, then $y=-2x+16$.

Step3: Analyze the system of equations

Since we don't know the first - line's equation precisely from the given graph, but we know the second - line's equation is $y=-2x + 16$. If the two lines are parallel (same slope), the system has no solution. If they are the same line, there are infinite solutions. If they intersect at a point, there is one solution. Without more information about the first line, we can only analyze the second - line's equation for now.

Answer:

C. The equation of the second line is $y=-2x + 16$; E. The system has no solution (assuming the first line has the same slope as the second line since no other information about the first line is given to suggest intersection or coincidence)