Math Problem Statement

Find an equation, in slope-intercept form, of the line shown in the graph.

Solution

To find the equation of the line in slope-intercept form (which is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept), we need to determine the slope and the y-intercept.

Step 1: Identify two points on the line.

From the image, it appears that two points on the line are:

  • (5,3)(-5, 3)
  • (1,0)(1, 0)

Step 2: Calculate the slope.

The slope mm is calculated by the formula: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Using the points (5,3)(-5, 3) and (1,0)(1, 0): m=031(5)=31+5=36=12m = \frac{0 - 3}{1 - (-5)} = \frac{-3}{1 + 5} = \frac{-3}{6} = -\frac{1}{2}

Step 3: Determine the y-intercept.

The slope-intercept form is y=mx+by = mx + b. We already know the slope m=12m = -\frac{1}{2}.

Now, substitute one of the points (let's use (1,0)(1, 0)) into the equation to solve for bb: 0=12(1)+b0 = -\frac{1}{2}(1) + b 0=12+b0 = -\frac{1}{2} + b b=12b = \frac{1}{2}

Step 4: Write the equation.

Thus, the equation of the line in slope-intercept form is: y=12x+12y = -\frac{1}{2}x + \frac{1}{2}

Would you like more details on this solution, or do you have any questions?

Here are 5 related questions:

  1. How do you find the slope if you are given only two points?
  2. What are the different forms of the equation of a line?
  3. How can you graph a line given its slope-intercept form equation?
  4. What does the slope represent geometrically?
  5. How can you convert the slope-intercept form to the standard form?

Tip: The y-intercept is the point where the line crosses the y-axis, and it occurs when x=0x = 0.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

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

Theorems

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Suitable Grade Level

Grades 8-10