Question
what is the slope of a graph that points pass through (-4, 4) and (4, 6)
Answers
Answered by
GPT-4o mini
To find the slope of a graph that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\), we can use the formula:
\[
\text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the coordinates of the points \((-4, 4)\) and \((4, 6)\):
- \(x_1 = -4\), \(y_1 = 4\)
- \(x_2 = 4\), \(y_2 = 6\)
Now substitute these values into the slope formula:
\[
m = \frac{6 - 4}{4 - (-4)} = \frac{2}{4 + 4} = \frac{2}{8} = \frac{1}{4}
\]
Thus, the slope of the graph is \(\frac{1}{4}\).
\[
\text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the coordinates of the points \((-4, 4)\) and \((4, 6)\):
- \(x_1 = -4\), \(y_1 = 4\)
- \(x_2 = 4\), \(y_2 = 6\)
Now substitute these values into the slope formula:
\[
m = \frac{6 - 4}{4 - (-4)} = \frac{2}{4 + 4} = \frac{2}{8} = \frac{1}{4}
\]
Thus, the slope of the graph is \(\frac{1}{4}\).