Question

Graph a line running through (2,3) with m=3/4.

Answer 1

In order to graph the line, plot the given point (2,3) on a coordinate plane. Then, use the slope of 3/4 to determine additional points on the line. For every 4 units you move horizontally to the right, move 3 units vertically upwards from the given point.

Step-by-step explanation:

To graph a line with a slope of 3/4 passing through the point (2,3), we can use the point-slope form of the equation of a line, which is:

y - y₁ = m(x - x₁ )

Here, (x₁ , y₁ ) represents the coordinates of the given point, and m represents the slope..

1. Substitute the given values into the point-slope form equation:

y - 3 = (3/4)(x - 2)

2. Distribute the (3/4) to the terms inside the parentheses:

y - 3 = (3/4)x - (3/4)(2)

3. Simplify the right side:

y - 3 = (3/4)x - 6/4

4. Combine the constants on the right side:

y - 3 = (3/4)x - 3/2

5. To isolate y, add 3 to both sides of the equation:

y = (3/4)x - 3/2 + 3

6. Simplify the equation further:

y = (3/4)x - 3/2 + 6/2

y = (3/4)x + 3/2

Now, we have the equation of the line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Connect the plotted points with a straight line, and label the line with its equation. You have now successfully graphed a line with a slope of 3/4 passing through the point (2,3).

Answer 2

To graph the line with a slope of 3/4 passing through (2, 3), plot the given point, use the slope to find a second point, and draw a straight line through both points. The slope indicates the rise over run, which is used to determine the position of the second point.

Step-by-step explanation:

Graphing a Line with Slope and a Point

To graph a line running through the point (2, 3) with a slope (m) of 3/4, start by plotting the given point on the Cartesian plane. The slope indicates that for every 4 units of horizontal movement (run), the line should rise by 3 units (rise). Therefore, from the point (2, 3), move 4 units to the right (increasing the x-value) and 3 units up (increasing the y-value) to find a second point. Plot this second point and draw a straight line through both points. This line represents the equation y - 3 = 3/4(x - 2), derived by applying the slope-intercept form (y = mx + b), where the y-intercept (b) can be calculated by substituting the x and y values of any known point on the line into the equation and solving for b.