Question

graph the equation
date 10/14/21 period 4
y = -\frac{3}{4}x - 5
y = 3x - 1
y = -2x + 4
y = \frac{1}{2}x + 2
write the equation of the line in slope intercept form

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: For $y=-\frac{3}{4}x - 5$

The slope $m =-\frac{3}{4}$ and the y - intercept $b=-5$. To graph, start at the point $(0, - 5)$ (the y - intercept) on the y - axis. Then, since the slope is $-\frac{3}{4}$, from the point $(0,-5)$ move 4 units to the right and 3 units down to find another point. Connect the points with a straight line.

Step3: For $y = 3x-1$

The slope $m = 3=\frac{3}{1}$ and the y - intercept $b=-1$. Start at the point $(0,-1)$ on the y - axis. Then move 1 unit to the right and 3 units up to find another point. Connect the points.

Step4: For $y=-2x + 4$

The slope $m=-2=-\frac{2}{1}$ and the y - intercept $b = 4$. Start at the point $(0,4)$ on the y - axis. Then move 1 unit to the right and 2 units down to find another point. Connect the points.

Step5: For $y=\frac{1}{2}x+2$

The slope $m=\frac{1}{2}$ and the y - intercept $b = 2$. Start at the point $(0,2)$ on the y - axis. Then move 2 units to the right and 1 unit up to find another point. Connect the points.

Step6: To find the equation of the line in the last graph

First, find the slope $m$. Let $(x_1,y_1)$ and $(x_2,y_2)$ be two points on the line. Suppose the line passes through $(0,6)$ and $(3,0)$. Then $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 6}{3-0}=\frac{-6}{3}=-2$. The y - intercept $b = 6$. The equation of the line in slope - intercept form is $y=-2x + 6$.

Answer:

The graphs of $y=-\frac{3}{4}x - 5$, $y = 3x-1$, $y=-2x + 4$, $y=\frac{1}{2}x+2$ are drawn as described above and the equation of the line in the last graph is $y=-2x + 6$.