# Given linear equation y = 0.5x – 2 a. find the y-intercept and slope. b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation. c. use two points to graph the equation.

Question
Linear equations and graphs
Given linear equation y = 0.5x – 2
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.

2020-11-06
(a) y-intercept and slope: In a linear equation y=b_0+b_1xZSK, the constant b1 be the slope and b0 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_1ZSK) 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 > 0ZSK, the slope of the linear equation $$\displaystyle{y}={b}_{{0}}+{b}_{{1}}{x}$$ is downward if $$\displaystyle{b}_{{1}}{<}{0}$$</span>, 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 $$\displaystyle{y}={0.5}{x}–{2},{b}_{{1}}$$ is 0.5, which is greater than 0.
Thus, the slope is upward.
(c) Graph by using two points:
The two points $$\displaystyle{\left({x}_{{1}},{y}_{{1}}\right)}{\quad\text{and}\quad}{\left({x}_{{2}},{y}_{{2}}\right)}$$ on the given line are obtained as follows:
If x=0
$$\displaystyle{y}={\left({0},{5}\times{0}\right)}-{2}$$
y=-2
Thus, one point on the line is $$\displaystyle{\left({x}_{{1}},{y}_{{1}}\right)}={\left({0},-{2}\right)}$$
If x=4,
$$\displaystyle{y}={\left({0.5}\times{4}\right)}-{2}$$
y=0
Thus, the second point on the line is $$\displaystyle{\left({x}_{{2}},{y}_{{2}}\right)}={\left({4},{0}\right)}$$

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