Example Question - calculating slope
Here are examples of questions we've helped users solve.
Calculating Slope and Y-Intercept from Graph
To find the slope and y-intercept of the line in the graph, we can use the following steps: **Slope:** The slope of a line is calculated by the rise over run. This means you need to determine how many units the line goes up (or down) for each unit it goes to the right. Looking at the graph, if we take two points on the line, for example, the point where it crosses the y-axis (the y-intercept) and any other point on the line, we can calculate the slope. From the graph, it looks like the line crosses the y-intercept at (0, 3) and goes through another point at (2, 7). Slope \( m = \frac{{change \, in \, y}}{{change \, in \, x}} = \frac{{y_2 - y_1}}{{x_2 - x_1}} \) So here, with our points (0, 3) and (2, 7): \( m = \frac{{7 - 3}}{{2 - 0}} \) \( m = \frac{4}{2} \) \( m = 2 \) The slope of the line is 2. **y-intercept:** The y-intercept is the point where the line crosses the y-axis. By inspecting the graph, the line crosses the y-axis at the point (0, 3). So the y-intercept is 3. Putting it all together, the slope is 2, and the y-intercept is 3.
Finding Linear Function through Two Points
To determine the linear function that goes through the points (3, -9) and (5, 13), we will use the slope-intercept form of a line, which is y = mx + b. Here, 'm' is the slope and 'b' is the y-intercept. First, calculate the slope (m) using the two points: m = (y2 - y1) / (x2 - x1) = (13 - (-9)) / (5 - 3) = 22 / 2 = 11 Now we have the slope, which is 11. Next, we use one of the points to find the y-intercept (b). Let's use point (3, -9) and substitute x and y into the equation along with our slope: -9 = 11 * 3 + b -9 = 33 + b b = -9 - 33 b = -42 Our linear function is y = 11x - 42.
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