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Difficulty: MediumLinear Equations and Graphing

A straight line graphed on a coordinate grid has a slope of 1.251.25 and passes through the point (4,11)(4, 11). If the point (k,−4)(k, -4) also lies on this line, what is the value of kk?

Answer: -8

Answer

The value of kk is −8-8.
The correct answer is −8-8. By using the point-slope formula of a line, we determine the equation to be y−11=1.25(x−4)y - 11 = 1.25(x - 4). Substituting the coordinates of the point (k,−4)(k, -4) yields the equation −4−11=1.25(k−4)-4 - 11 = 1.25(k - 4). Solving this equation results in k=−8k = -8.

Step-by-Step Solution

1
Use the point-slope formula of a line, y−y1=m(x−x1)y - y_1 = m(x - x_1), to write the equation of the line.
y−11=1.25(x−4)y - 11 = 1.25(x - 4)
We are given the slope m=1.25m = 1.25 and a point (4,11)(4, 11) on the line.
2
Substitute the coordinates of the second point, (k,−4)(k, -4), into the line's equation.
−4−11=1.25(k−4)-4 - 11 = 1.25(k - 4)
Since the point (k,−4)(k, -4) lies on the line, its coordinates must satisfy the line's equation.
3
Solve the equation for kk.
k=−8k = -8
Simplify the left side to get −15=1.25(k−4)-15 = 1.25(k - 4), divide both sides by 1.251.25 to get −12=k−4-12 = k - 4, and add 44 to both sides to find k=−8k = -8.

Key Concept

Writing and solving linear equations using point-slope form.
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Topics

Linear Equations and Graphing

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