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Use the graph to answer the question.

Write the equation of the line shown in the graph in slope-intercept form.

A coordinate plane going from negative 10 to 10 in increments of 1 labeled every 5 units on the x- and y-axes.

(1 point)
The equation in slope-intercept form is $$
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3 answers

To write the equation of the line in slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), you will need the following:

  1. Identify the slope (m): The slope of the line can be calculated using two points on the line. The formula for slope is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

  2. Identify the y-intercept (b): This is the point where the line crosses the y-axis. This is the value of \(y\) when \(x = 0\).

If you have specific points identifiable on the graph or the exact location of the line, you can substitute those into the formula to find \(m\) and \(b\).

For example, if the line passes through the points \((1, 2)\) and \((3, 4)\):

  • Calculate the slope: \[ m = \frac{4 - 2}{3 - 1} = \frac{2}{2} = 1 \]

  • Find the y-intercept (b) from one of the points. If the line goes through \((1, 2)\): \[ b = 2 - 1 \cdot 1 = 1 \]

Thus, the equation of the line would be: \[ y = 1x + 1 \quad \text{or simply} \quad y = x + 1. \]

If you provide specific points or features of the graph, I can assist you in determining the actual equation based on that information!

the points on the graph on (-2, 1) and (2, 3)

Great! Let's use the points \((-2, 1)\) and \((2, 3)\) to find the equation of the line in slope-intercept form.

  1. Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, you can let \((x_1, y_1) = (-2, 1)\) and \((x_2, y_2) = (2, 3)\).

    \[ m = \frac{3 - 1}{2 - (-2)} = \frac{2}{2 + 2} = \frac{2}{4} = \frac{1}{2} \]

  2. Find the y-intercept (b). We can use one of the points to find \(b\). Using the point \((-2, 1)\): \[ y = mx + b \implies 1 = \frac{1}{2}(-2) + b \] Simplifying, \[ 1 = -1 + b \implies b = 1 + 1 = 2 \]

  3. Write the equation in slope-intercept form (y = mx + b): \[ y = \frac{1}{2}x + 2 \]

So the equation of the line in slope-intercept form is: \[ \boxed{y = \frac{1}{2}x + 2} \]