Question

Select all the points that are on the graph of the line 2.1 + 4y = 20

(0,5)
(0, 10)
(1, 2)
(1, 4)
(5, 0)
(10,0)

Answer 1

None of the given points lie on the line represented by the equation 2.1 + 4y = 20. Upon converting the equation to slope-intercept form, it is clear that each provided point does not satisfy the equation y = 4.475.

Step-by-step explanation:

To verify which of the given points lies on the graph of the line 2.1 + 4y = 20, we first solve for y to find the linear equation in slope-intercept form (y = mx + b). Subtracting 2.1 from both sides gives us 4y = 17.9. We then divide by 4, which simplifies to y = 4.475. This means for any x-value, the corresponding y-value must equal 4.475 for the point to be on the line. Let's examine the given points.

• (0,5): Substituting x=0 into the equation y = 4.475 does not yield y=5, so this point is not on the line.
• (0, 10): Substituting x=0 into the equation does not yield y=10, so this point is also not on the line.
• (1, 2): The equation y = 4.475 does not depend on x, so this point is also not correct.
• (1, 4): This is also incorrect, as y must be 4.475, not 4.
• (5, 0): If y is zero, the equation 4y = 17.9 is not satisfied, so this point is not correct.
• (10,0): This point is also not on the line for the same reason as the previous point.

We can conclude that none of the provided points are on the graph of the given line.