Which is a solution of the equation y = 4x + 3?
(1 point)
(5, 17)
(17,5)
(4, 19)
(4, 16)
The Correct Answer and Explanation is :
The equation given is ( y = 4x + 3 ), which is in the slope-intercept form of a linear equation, where ( y ) is the dependent variable, ( x ) is the independent variable, and the slope is 4, while the y-intercept is 3.
We are tasked with determining which of the following ordered pairs is a solution to this equation:
- (5, 17)
- (17, 5)
- (4, 19)
- (4, 16)
Step-by-Step Process to Check Each Option:
- Substitute ( x = 5 ) into the equation ( y = 4x + 3 ): [
y = 4(5) + 3 = 20 + 3 = 23
] So, for ( x = 5 ), ( y ) should be 23. The point (5, 17) does not satisfy this equation because the y-value is 17, not 23. Therefore, (5, 17) is not a solution. - Substitute ( x = 17 ) into the equation ( y = 4x + 3 ): [
y = 4(17) + 3 = 68 + 3 = 71
] So, for ( x = 17 ), ( y ) should be 71. The point (17, 5) does not satisfy this equation because the y-value is 5, not 71. Therefore, (17, 5) is not a solution. - Substitute ( x = 4 ) into the equation ( y = 4x + 3 ): [
y = 4(4) + 3 = 16 + 3 = 19
] So, for ( x = 4 ), ( y ) should be 19. The point (4, 19) satisfies the equation. Therefore, (4, 19) is a solution. - Substitute ( x = 4 ) into the equation ( y = 4x + 3 ): [
y = 4(4) + 3 = 16 + 3 = 19
] So, for ( x = 4 ), ( y ) should be 19. The point (4, 16) does not satisfy this equation because the y-value is 16, not 19. Therefore, (4, 16) is not a solution.
Conclusion:
The correct solution to the equation ( y = 4x + 3 ) is the point (4, 19), as substituting ( x = 4 ) into the equation results in ( y = 19 ), which matches the second value of the ordered pair.