Math Problem Statement

The point with coordinates (d, 4) lies on the line shown. What is the value of d?

Solution

We are given the point (d,4)(d, 4) that lies on the line shown in the graph, and we need to find the value of dd.

Step 1: Determine the equation of the line.

From the graph, two points on the line are clearly visible:

  • (0,8)(0, 8)
  • (8,0)(8, 0)

The slope mm of the line can be calculated using the slope formula: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Substituting the points (0,8)(0, 8) and (8,0)(8, 0): m=0880=88=1m = \frac{0 - 8}{8 - 0} = \frac{-8}{8} = -1

Step 2: Write the equation of the line in slope-intercept form.

The slope-intercept form is: y=mx+by = mx + b We know the slope m=1m = -1 and the y-intercept b=8b = 8, since the line crosses the y-axis at y=8y = 8. So, the equation of the line is: y=x+8y = -x + 8

Step 3: Find the value of dd.

The point (d,4)(d, 4) lies on this line, meaning it satisfies the equation. Substituting y=4y = 4 into the equation: 4=d+84 = -d + 8 Solving for dd: d=48-d = 4 - 8 d=4-d = -4 d=4d = 4

Thus, the value of dd is 44.

However, upon reviewing the answer choices, d=4d = 4 is not listed. Therefore, it's likely the graph contains a misinterpretation or the printed options don't fully match. In this specific case, no correction matches d = 4. Is there a chance we can try partier correct for response selecting among markedforms

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Coordinate Geometry

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)
Equation of a line: y = mx + b

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 8-10