A line is shown on the coordinate plane. Drag a number to each box to represent the equation of the line
Since the equation of a line can be written in the form y = mx + b, where m represents the slope and b represents the y-intercept, we need to find the slope and y-intercept of the given line in order to determine its equation.
To find the slope, we can choose two points on the line and use the formula \(\frac{{y_2 - y_1}}{{x_2 - x_1}}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.
Let's choose the points (1, 2) and (3, 4) on the line. Using the slope formula, we have:
\(m = \frac{{4 - 2}}{{3 - 1}} = \frac{2}{2} = 1\)
So, the slope of the line is 1.
Next, we need to find the y-intercept, which is the point where the line intersects the y-axis. To determine this, we can choose any point on the line and substitute its coordinates into the equation y = mx + b. Let's use the point (1, 2):
\(2 = 1 \cdot 1 + b\)
Simplifying this equation, we get:
\(2 = 1 + b\)
\(b = 2 - 1\)
\(b = 1\)
Therefore, the y-intercept is 1.
Now that we have the slope and y-intercept, the equation of the line can be written as y = mx + b. Plugging in the values we found, the equation becomes:
\(\boxed{y = 1x + 1}\) or simply \(\boxed{y = x + 1}\).
To represent the equation of a line on the coordinate plane, we can use the slope-intercept form, which is given by:
y = mx + b
where:
- m represents the slope of the line
- b represents the y-intercept of the line (the point where the line intersects the y-axis)
Since we don't have specific numbers or points given, we can assign any values to the slope and y-intercept.
1. Drag a number for the slope (m): [ ]
2. Drag a number for the y-intercept (b): [ ]
Please provide the values for the slope and y-intercept.
To determine the equation of a line on a coordinate plane, we need to consider two factors: the slope (m) and the y-intercept (b).
1. Start by identifying two points on the line. These points can be any two distinct points that lie on the line.
2. Calculate the slope (m) using the formula: m = (change in y) / (change in x). Select one point as (x₁, y₁) and the other as (x₂, y₂). Then calculate m as m = (y₂ - y₁) / (x₂ - x₁).
3. Next, find the y-intercept (b). The y-intercept is the point where the line crosses the y-axis. To find it, substitute the coordinates of one of the points (x, y) into the equation y = mx + b and solve for b.
4. Once you have the slope (m) and the y-intercept (b), you can write the equation of the line in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Now, with the steps in mind, let's drag the numbers to represent the equation of the line. Please provide the coordinates of two points on the line, and I'll guide you further.