graph the line with the equation $y = -\\frac{3}{4}x + 5$.

graph the line with the equation $y = -\\frac{3}{4}x + 5$.

graph the line with the equation $y = -\\frac{3}{4}x + 5$.

Answer

Answer:

To graph the line $y =-\frac{3}{4}x + 5$, we can follow these steps to plot points and draw the line.

  1. Find the y - intercept:
    • The equation of the line is in slope - intercept form $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept.
    • For the equation $y =-\frac{3}{4}x + 5$, when $x = 0$, $y=5$. So the y - intercept is the point $(0,5)$. Plot this point on the graph.
  2. Use the slope to find another point:
    • The slope $m=-\frac{3}{4}$. The slope is the ratio of the change in $y$ to the change in $x$ ($m=\frac{\Delta y}{\Delta x}$).
    • Starting from the y - intercept $(0,5)$, since the slope is $-\frac{3}{4}$, we can move 4 units to the right (increase $x$ by 4) and 3 units down (decrease $y$ by 3).
    • When $x=4$, $y=-\frac{3}{4}\times4 + 5=-3 + 5 = 2$. So another point on the line is $(4,2)$. Plot this point on the graph.
  3. Draw the line:
    • Connect the two points $(0,5)$ and $(4,2)$ with a straight line. This line represents the graph of the equation $y =-\frac{3}{4}x+5$.

Explanation:

Step1: Identify the y - intercept

When $x = 0$, $y=5$ as per $y=-\frac{3}{4}x + 5$.

Step2: Use the slope to find a second point

Slope $m =-\frac{3}{4}$, moving 4 units right ($x$ changes from 0 to 4) and 3 units down ($y$ changes from 5 to 2).

Step3: Draw the line

Connect the points $(0,5)$ and $(4,2)$ with a straight - line.