Math Problem Statement

Write an equation in slope-intercept form of the line (use integers or fractions for any numbers in the equation).

Solution

From the image, the task is to write an equation in slope-intercept form of the line shown on the graph. The slope-intercept form of a line is expressed as:

y=mx+by = mx + b

where mm is the slope and bb is the y-intercept.

Let's determine the slope (mm) first. The slope can be calculated by selecting two points on the line and using the formula:

m=change in ychange in x=y2y1x2x1m = \frac{\text{change in y}}{\text{change in x}} = \frac{y_2 - y_1}{x_2 - x_1}

From the graph, we can select the points (1, 3) and (3, 1). Plugging these into the formula:

m=1331=22=1m = \frac{1 - 3}{3 - 1} = \frac{-2}{2} = -1

Next, the y-intercept (bb) is the point where the line crosses the y-axis. Observing the graph, the line crosses the y-axis at y=5y = 5. Therefore, b=5b = 5.

Combining these, the equation of the line in slope-intercept form is:

y=1x+5y = -1x + 5

Or simply:

y=x+5y = -x + 5

Would you like more details on how to find the slope or y-intercept from a graph? Do you have any questions?

  1. Would you like to see another example of writing an equation from a graph?
  2. Do you need clarification on how the y-intercept is identified on a graph?
  3. Are you interested in learning about different forms of linear equations?
  4. Would you like to know how to check if a point lies on this line?
  5. Are there other types of equations or graphs you're curious about?

Tip: When choosing points from a graph to calculate the slope, it's often useful to pick points where the line crosses grid lines to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

y = mx + b
Slope Formula: m = (y2 - y1) / (x2 - x1)

Theorems

Slope-Intercept Form of a Line

Suitable Grade Level

Grade 8-9