Question

graph the line.
$y = -dfrac{3}{4}x - 1$

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=-\frac{3}{4}x - 1\), the slope \(m =-\frac{3}{4}\) and the y - intercept \(b=- 1\).

Step2: Plot the y - intercept

The y - intercept is \(b = - 1\), so we plot the point \((0,-1)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m=-\frac{3}{4}=\frac{\text{rise}}{\text{run}}\). This means from the point \((0, - 1)\), we can go down 3 units (because the rise is - 3) and then to the right 4 units (because the run is 4). So from \((0,-1)\), moving down 3 gives \(y=-1 - 3=-4\) and moving right 4 gives \(x = 0+4 = 4\). So we get the point \((4,-4)\). We can also go up 3 units and left 4 units from \((0,-1)\): \(y=-1 + 3=2\) and \(x=0 - 4=-4\), giving the point \((-4,2)\).

Step4: Draw the line

Connect the points (for example, \((0,-1)\), \((4,-4)\) and \((-4,2)\)) with a straight line.

(Note: Since the problem is about graphing, the final answer is the graph of the line \(y =-\frac{3}{4}x-1\) passing through the points like \((0, - 1)\), \((4,-4)\), \((-4,2)\) etc. on the given coordinate plane.)

Answer:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=-\frac{3}{4}x - 1\), the slope \(m =-\frac{3}{4}\) and the y - intercept \(b=- 1\).

Step2: Plot the y - intercept

The y - intercept is \(b = - 1\), so we plot the point \((0,-1)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m=-\frac{3}{4}=\frac{\text{rise}}{\text{run}}\). This means from the point \((0, - 1)\), we can go down 3 units (because the rise is - 3) and then to the right 4 units (because the run is 4). So from \((0,-1)\), moving down 3 gives \(y=-1 - 3=-4\) and moving right 4 gives \(x = 0+4 = 4\). So we get the point \((4,-4)\). We can also go up 3 units and left 4 units from \((0,-1)\): \(y=-1 + 3=2\) and \(x=0 - 4=-4\), giving the point \((-4,2)\).

Step4: Draw the line

Connect the points (for example, \((0,-1)\), \((4,-4)\) and \((-4,2)\)) with a straight line.

(Note: Since the problem is about graphing, the final answer is the graph of the line \(y =-\frac{3}{4}x-1\) passing through the points like \((0, - 1)\), \((4,-4)\), \((-4,2)\) etc. on the given coordinate plane.)