using the graph, to derive the equation of the line in slope-intercept form.
(1 point)
y=3x+4
y=3x-4
y=-3x-4
3x-y=4
To derive the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b) from the graph.
Looking at the given equations, we can identify the equation in slope-intercept form as y = 3x + 4. This equation has a slope of 3 and a y-intercept of 4.
write the equation of the line in slope-intercept form.
(1-point)
y=-5x + 1
-5x -y= -1
y= -5x -1
y=5x + 1
The equation of the line in slope-intercept form is y = -5x + 1. This equation has a slope of -5 and a y-intercept of 1.
To derive the equation of the line in slope-intercept form, we need the equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.
Given the equation options, let's assess each one:
1) y = 3x + 4
2) y = 3x - 4
3) y = -3x - 4
4) 3x - y = 4
By comparing these options to the slope-intercept form, we can see that option 1, y = 3x + 4, is already in slope-intercept form, so that is the correct answer.
Therefore, the equation of the line in slope-intercept form is y = 3x + 4.
To determine the equation of a line in slope-intercept form, we need the slope (m) and the y-intercept (b). The slope-intercept form of a line is given by the equation y = mx + b.
Let's use the provided graph to determine the equation of the line. Remember, the slope (m) is the ratio of the vertical change (Δy) to the horizontal change (Δx) between any two points on the line.
Looking at the graph, we can see that the line passes through the point (0, 4). This point represents the y-intercept (b) as it intersects the y-axis when x = 0. Therefore, b = 4.
Now, let's find the slope (m) using two points on the line. Pick any two points on the line and calculate the slope by dividing the change in y by the change in x.
Let's select the points (1, 7) and (2, 10) on the line. The change in y is 10 - 7 = 3, and the change in x is 2 - 1 = 1. So, the slope (m) is 3/1 = 3.
We now have the slope (m) as 3 and the y-intercept (b) as 4. Plugging these values into the slope-intercept form equation, we get:
y = 3x + 4
Therefore, the correct equation of the line, represented by the graph, is y = 3x + 4.