Question Bank / Math / Linear Equations in Two Variables

Linear equations in two variables SAT question

Math · Algebra · Hard · Answer it here, explanation included.

x	y
3	7
k	11
12	n

The table above shows the coordinates of three points on a line in the xy-plane, where k and n are constants. If the slope of the line is 2, what is the value of $k plus n$ ?

Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.

ExplanationShow

The correct answer is 30. The slope of a line can be found by using the slope formula, $the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction$ . It’s given that the slope of the line is 2; therefore, $the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction, equals 2$ . According to the table, the points $with coordinates 3 comma 7$ and $with coordinates k comma 11$ lie on the line. Substituting the coordinates of these points into the equation gives $the fraction with numerator 11 minus 7, and denominator k minus 3, end fraction, equals 2$ . Multiplying both sides of this equation by $k minus 3$ gives $11 minus 7, equals, 2 times, open parenthesis, k minus 3, close parenthesis$ , or $11 minus 7, equals, 2 k minus 6$ . Solving for k gives $k equals 5$ . According to the table, the points $with coordinates 3 comma 7$ and $with coordinates 12 comma n$ also lie on the line. Substituting the coordinates of these points into $the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction, equals 2$ gives $the fraction with numerator n minus 7, and denominator 12 minus 3, end fraction, equals 2$ . Solving for n gives $n equals 25$ . Therefore, $k plus n, equals, 5 plus 25$ , or 30.

Drill this skill on Aceit

Adaptive practice, a daily plan, and score tracking take a free account so we can save your work.

Practice this skill

Linear equations in two variables SAT question

More Linear equations in two variables questions