Given linear equation y = 0.5x – 2 a. find the y-intercept and slope. b....

(a) y-intercept and slope: In a linear equation $y=b_0+b_{1}x$, the constant $b1$ be the slope and $b_0$ be the y-intercept form and x is the independent variable and y is the dependent variable. Comparing the given equation with the general form of linear equation the slope of the equation is 0.5 and the y-intercept is –2. Therefore, the y-intercept is –2 and the slope of the linear equation (b_1) is 0.5. (b) It is known that, the slope of the linear equation ${\displaystyle y=b_0+b_{1}x}$ is upward if b_1 > 0, the slope of the linear equation ${\displaystyle y=b_0+b_{1}x}$ is downward if ${\displaystyle b_1<0}$, and the slope of the linear equation ${\displaystyle y=b_0+b_{1}x}$ is horizontal if ${\displaystyle b_1=0}$ .
Thus, in the given equation ${\displaystyle y=0.5x–2,b_1}$ is 0.5, which is greater than 0.
Thus, the slope is upward.
(c) Graph by using two points:
The two points ${\displaystyle (x_1,y_1)\text{and}(x_2,y_2)}$ on the given line are obtained as follows:
If x=0
${\displaystyle y=(0,5\times 0)-2}$
y=-2
Thus, one point on the line is ${\displaystyle (x_1,y_1)=(0,-2)}$
If x=4,
${\displaystyle y=(0.5\times 4)-2}$
y=0
Thus, the second point on the line is ${\displaystyle (x_2,y_2)=(4,0)}$