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 \(\boxed{y = x + 1}\).
A line is shown on the coordinate plane. Drag a number to each box to represent the equation of the line
1 answer
1 answer